https://en.wikipedia.org/wiki/Treaty_of_Turin_(1860)
"And yet, in view of all these most solemn assurances, what have we seen? Italian troops removed and French troops put in their places; all the important civil offices filled with Frenchmen, or men committed to the support of the French cause; official circulars and placards advocating annexation scattered everywhere, while no publication of an opposing sentiment was anywhere allowed; ballot-boxes in exclusive control of French officers; ballots in favor of annexation distributed everywhere by the police, while ballots opposed to annexation could be procured only by sending to Geneva; priests blessing the flags presented by the Emperor, and appealing to the consciences of their people in behalf of France; money, as well as general free living and drinking, furnished by the imperial agents; and, finally, the people, with French music sounding and French banners flying, marched up en masse to the ballot-box, with priest and mayor arm-in-arm at their head. Such was the boasted "free vote" with the sanction and help of which Nice and Savoy were annexed to France."
Obviously it wasn't wholly accepted as Mussolini hated it, but how "Free & Fair" was the vote? Is that as rigged as it sounds? Why was it accepted(not the trade of nice and savoy for support, that just seems like politics), but the plebiscite's legitimacy?
It appears that you are quoting Charles Kendall Adams here - rather than the wikipedia entry that bizarrely enough declares itself "based on the corresponding French entry" while it is instead fairly different.
I am fully unfamiliar with his stature as a historian - and I'll therefore assume he is as reputable as his standing among his peers suggested when he was made President of the AHA in 1889. But this citation seems to be coming from his collection Democracy and monarchy in France from the inception of the great revolution to the overthrow of the second empire [1874-75], whose angle seems to be a (legitimate) challenge of the democratic clothing of Louis Napoleon's Third Empire.
With this in mind, I am not sure it would be fair to rely entirely on his judgment on the "honesty" of the plebiscite. A plebiscite is - in common use - almost a derogatory term, to mark a popular vote that is, in its intrinsic formulation, or due to the surrounding circumstances, rigged in such way as to provide not only the desired outcome, but one that leaves no margin of recrimination.
Here it appears that the author is more interested in the general modes of such a process, rather than calling into question its value as a representation instrument - fair and square though, there was in 1860 no issue of representation in Italy, and the accomodation of the "plebiscites" served more to retain some semblance of the French Emperor's republican aura. It's curious that the wikipedia entry again points out that the plebiscite was "restricted to adult males" (as if that was uncommon) - while that choice would have appeared to an Italian observer most likely an abuse of popularism: the Italian electoral law (1861) gave the right of vote to males over 25 years of age, literate, and above a certain level of fiscal contribution (so that the electoral body was less than 2% of the population). With this in mind it's a bit disingenuous to call the plebiscite dishonest, as if those people would have had any way to make their opinion on the matter count otherwise.
Of course there were those who opposed it - the Italian local notables, who certainly saw their position of privilege challenged by the French domination; certain groups of French-speaking loyalist (the "Piedmontese" party as was called at the time) who saw in the loss of the French portions of Piedmont a sign of the weakening of the Piedmontese character within the Italian context. Garibaldi obviously was against it - he was after all from Nice, and still (despite his apparent acquiescence to the King) a republican - and his parliamentary speech on the matter made some echo, but no lasting effect.
Garibaldi himself had greater things in his mind though, since immediately after his resignation (third week of April 1860) he had begun the preparations for his "expedition of one thousand" to Sicily (early May) - where soon after his arrival, a plebiscite for the unification was arranged under the supervision of the (initially reluctant) pro-dictator Antonio Mordini.
The Sicilian plebiscite took place in October and sanctioned the annexation to the future Kingdom of Italy with a 99.85% of favorable votes. Meanwhile a similar plebiscite had taken place in Tuscany, with a somewhat disappointing 96.10% in favor of the annexation.
For sake of completeness, Nice voted yes with 99.4% and Savoy with 99.8%.
Well above 99% had been the results of the plebiscites for the annexation in Modena, Parma and the Papal States held during 1860.
Those sort of results were expected; in fact the popular desire to join one nation or another one was not the crucial matter at hand (Kings and Emperors had seen to the matter of annexations themselves; "the King makes the foreign policy", as per the Italian Statute and per Victor Emmanuel's own well established belief) - since the popular desire found no expression within the government of the country, by reason of its representative system. At the same time, I don't think it's correct to derive from this point (like many have done over the years, and frequently for fairly non democratic reason, I dare say) the idea that those acts were against the will of the populace. Since a will of the populace, in the form of a coherent political action, was something the regional and national elites had various substantial reasons to doubt even existed (and I would be dishonest if I dismissed their point of view entirely out of hand as preconceived notions and self interests).
The "era of the plebiscites" was at a crossing mark between an age where the will of the people was "nothing at all" and another one where it begun to be taken as the true foundation of the political forms of the state (for completeness again, universal male suffrage came to Italy only in 1913). For this reason it had an intrinsic nature of compromise, and often an instrumental one: reading through the words of the men in charge of those events (Crispi, Farini, Cavour, D'Azeglio, Ricasoli, etc.), you can see their awareness of dealing with some greater principles that they can't really fit onto their surrounding reality. Their desire to have an Italian nation, with an Italian people behind it - and their concern with how dangerous even a partial insuccess may have appeared (in the age of plebiscites, the 96.10% of Tuscany was taken as a sign of discomfort). They had to rely on the instrument of popular legitimation, in a context where popular political participation was something they could not expect, endorse without fear of negative repercussions, nor likely recognize if they saw it in action.
Farini spoke ill-words of the Neapolitan population - ready to support any group willing to pay them, or misled by superstition and slander. The Sicilian men voted as their Baron, or land-owner (after the suppression of titles), told them to. They did so largely because that was the authority they recognized in their lives - the source of their political truth, the voice of "honesty".
From this angle, we may (and I say may for obvious reasons) agree with Adams that the United States were a bit ahead on the road, but we should not discount the fact that those plebiscites - no matter how staged, convenient, and unfair they may appear to us - marked the first time those people had been called to act as a source of legitimacy of the State's authority. The implicit idea was completely obscure to most of them - and it's fair to say that most of the republican and anti-Monarchical literature looked at them in a negative light - but it should be not lost on us, if we look for honesty.
I have put this together on the fly, taking bits here and there from Candeloro, Isnenghi, Mack Smith, etc. - there's more to be said about the plebiscites as a political instrument and their relevance within the formation of the new theory of national states (see the usual works of Pasquale Stanislao Mancini), even in a European context, and maybe someone will add more the internal French side of things.
Last of it, Mussolini's objection to unfair plebiscites - whether he actually rose the argument in those terms, I am not sure - would be something!
And I find a bit odd that the Wikipedia entry tells us that "The late King Charles Albert of Sardinia (1798–1849) had been an active Italian nationalist" - which may even be true, in some way.