Your friend is quite wrong.

Pace Tom Nairn's The Enchanted Glass, the twentieth-century British royal family has had very little power over civilian governments. In theory, Queen Elizabeth II could disband parliament and nominate one of her corgis as PM (which might be an improvement for contemporary UK politics!) but these would destroy whatever prestige the monarchy has left in the UK. The Romanovs in the late-nineteenth and early-twentieth centuries were far more powerful heads of states and not mere figureheads.

It needs to be emphasized that the Russian imperial government was more than its autocratic head. Various parts of the vast imperial state governed without direct input from the St. Petersburg and the absolute power of the tsars was more nominal than real. This was a function of the growing size and complexity of the modern industrial state which needed a vast corpus of trained officials to run it. Nonetheless, the Romanov royal family did play an outsized role within the imperial government. The emperor made imperial appointments for various governorships and various scions of the royal family were placed in important government positions throughout the empire. The emperors' ability to summon and dismiss high officials was one of the crucial levers of Romanov power and prestige.

The problem here for Nicholas II was that the ethos of the autocratic state was very much at odds with the needs of a modern state. As Dominic Lieven noted in an LSE lecture, Russia was the "t-rex of reaction," meaning that the Romanovs positioned themselves as the levee against the various political changes unleashed by the French Revolution. These post-1789 tides ranged from liberalism, nationalism, rising education, and later included modern capitalism and industrialization. The Romanovs' default position was to oppose all of these changes because they potentially undercut the power and prerogatives of the absolutist state. For example, the Russian imperial state had a strained relationship with Great Russian nationalist activists. While the latter valorized the Romanovs as one of the pillars of holy Russia, it was difficult for the Romanovs to assume the Russian nationalist mantle. Although national identity was very protean, the 1897 census of the empire showed that Great Russians at best consisted of 40% of the empire's population. Being a Great Russian emperor opened up the can of worms of what to do about the rest of empire's non-Russian subjects.

There were similar contradictions riven through the whole of late-imperial sociopolitical culture. The late imperial economy grew at a staggering rate, but the government itself was spectacularly ill-equipped to deal with the rise of new men among the nascent industrial classes. The soslovie system of social ranks worked reasonably well for a pre-industrial political order, but it really could not accommodate these new social conditions. Russia's nouveau riche could not advance up the social ladder and bridge the gap between business and government given that such power would undermine the very system of autocracy. Nor were the new masses of the proletariat something that the imperial estate system could easily stomach; unlike the agrarian peasantry, the new working classes were more mobile (both literally and figuratively) and less attached to traditionalism. One of the dilemmas of Nicholas II was that he could not engage in substantive modern reforms such as countenancing a constitutional order but Russia needed to be a modern state to remain a relevant great power.

The patchwork nature of the Great Reforms of Nicholas II's grandfather and the neo-absolutist turn of his father did buy Nicholas II's autocracy some degree of time. The tenuous European geopolitical stability of the late-nineteenth century also ensured that there were no major foreign crises to upset the delicately balanced imperial order. But the empire was not a terribly healthy polity as it, in the memorable words of Stephen Kotkin, "choked on the very modernity that it desperately needed and, to an extent, pursued in order to compete as a great power." Nicholas II increasingly governed via a series of skirted decisions prior to the 1905 Revolution. But the contradictions of an archaic political order kept piling up. The imperial state often used Great Russian nationalists for political dirty work, but the empire's government could never sate various slavophile demands.

In hindsight, it would have taken a political genius to work out this system. Nicholas II was not such a figure. He relied very heavily on the delegation of authority to various servitors, but he was often at odds with their independence. This was clear with the Emperor's treatment of Stolypin after the 1905 Revolution. Stolypin was arguably the one figure most responsible for stabilizing the revolutionary chaos through harsh and murderous methods but Nicholas II never fully trusted the man. This meant that Stolypin's attempts to craft a neo-conservative order had a powerful enemy and Stolypin was vulnerable to any intrigues. Nicholas II had no real substitute vision of how the autocratic state could function in the modern era though. He never could abide even the extremely limited power of the Duma and his dismissal of the body on several occasions only made him more political enemies among what could have been allies of a reformist tsar.

It is true that the subsequent Soviet state would be more dictatorial and violent than its tsarist predecessor. Lenin's Siberian exile was far more comfortable treatment than what the USSR would mete out to political enemies and the Cheka/NKVD/KGB was a far more invasive and ruthless secret police force than the tsarist Okhrana. But that was in the future. By the standards of its contemporaries imperial Russia was the most repressive and dictatorial of the major powers of the world in the early-twentieth century. The aforementioned Okhrana may not have been as powerful as its successors, but its excesses were not fictions. The state had next to no legal or constitutional checks on its behavior and this led to violence being a normal tool of political repression. The "Stolypin necktie" (the liberal use of arbitrary capital punishment) was one of the main methods tsardom used to reestablish its authority after 1905. This was part of a larger process of normalizing violence as an essential adjunct to political power within the empire. The pogroms against Russia's Jews were just one symptom of this trend and although the imperial state did not directly encourage these ethnic cleansings, imperial policies treating Jews as outsiders, restricting their movement within the empire, and a host of other repressive measures added tinder to combustible ethnic tensions.

As the autocrat of the imperial state, Nicholas II bears a good deal of responsibility for this state of affairs. He may not have authorized pogroms, but he did preside over many of the conditions that made them possible. The Bolsheviks were very much a symptom of the deliberately archaic political order tsardom encouraged against its better interests. While it became a staple of anti-Bolshevik circles that Russia was doing fine until 1917 and would have reformed itself had those pesky revolutionaries not intervened, the facts on the ground say otherwise. Going into 1914, there was little love for Nicholas II even among potential allies of a constitutional monarchy such as the Kadets. There was a reason why the abdication and abolition of the monarchy in the wake of the February Revolution was accomplished with so little fanfare.

Let me jump in a little on question #2: why would a Russian emigre family believe this, especially if they're highly educated?

Now I can't speak to their particular background - if they were an Emigre entire family (by which I mean they or their ancestors left during or after the Civil War, because of opposition to the Bolsheviks), then it might not be so surprising that they would feel this way about the tsar and his family. Note: I see there are parents living in Russia so probably this isn't the case, but it's worth noting that there was a significant anti-Bolshevik winger community outside the USSR throughout the Soviet period.

It's also worth noting that Russia as a whole rehabilitated Tsar Nicholas II and his family, as well as tsarist symbols, starting in 1990 and after the end of the Soviet Union. It's why you get the modern incongruity of the statist double headed eagle, the Republican Provisional Government tricolor flag, and the Soviet red star all being used as state symbols simultaneously.

After Nicholas II and his family's remains were recovered from their burial spots near Yekaterinburg and were positively identified by DNA testing, they were reburied at the St Peter and Paul Cathedral in St Petersburg on the 80th anniversary of their deaths in 1998. Boris Yeltsin originally did not plan to attend, but eventually did and gave a eulogy describing their killings as a "monstrous crime" and a "sin" requiring repentance (he was from Yekaterinburg, by the way). Weirdly the Patriarch of the Russian Orthodox Church did not accept the DNA results as valid and boycotted the service, and then held his own memorial service in Moscow when the Romanov family complained the St. Petersburg service wasn't grand enough.

Of course the rehabilitation of the tsar and his family did not stop with their mortal remains, but also extended to their immortal souls. The Russian Orthodox Church Outside Russia, established in the 1920s and which served as a sort of anti-Soviet emigre church, canonized the family in 1981, which the Russian Orthodox Church disputed by claiming that they did not specifically die for religious reasons. Something of a compromise was reached in 2000 when the Russian Orthodox Church declared them "passion bearers" but not saintly martyrs per se, and seeing as how the Russian Orthodox Church Outside Russia merged with the Russian Orthodox Church in 2007 that would seem to be that.

Since 1991 and continuing to the present, official Russian historiography has awkwardly tried to deal with all of these conflicting strands of Russian history, usually by accenting the positives and downplaying the negatives. This is one reason why the centenaries of both Russian Revolutions passed last year with essentially no public comment, while Victory Day gets the full treatment: although again, it involves incongruously playing Soviet military music and marching a Soviet banner (the Victory Banner, shown for historic purposes of course) past an icon of St. George that the Minister of Defense noticeably crosses himself under.

Vera Hold and Wendy Slater both have a couple of great essays on the incongruity of historic symbols in post communist Russia, and also on the disconnect between official and private history - this is really where I was trying to with this answer!

Let me end by unpacking that last one a little, courtesy of Slater: she notes that among the Russian population there is a general cynicism and distrust of "history", in that it implies something official that the government is forcing citizens to learn, regardless of how true it is. This is completely separated from a relatively strong popularity for memoirs and biographies (so maybe something more like what we'd call "social history") which ironically had been encouraged by the Soviet regime at various points promoting the keeping of diaries and memoirs by regular citizens (the better to document the building of Soviet civilization!). So there is a strong popularity for accounts of suffering and survival of individuals outside of and at the hands of history, which always seems to come from someone/somewhere else (as an aside I think you can see this outlook even in the Russian language, where you can talk about "they" doing something without even using a pronoun).

So there is something appealing to thinking the Romanov family being just a family of personally good people with not that much real power getting caught up in the forces of history and tragically suffering because of it, just like everyone else.