The message coming out of the Soviet Union regarding independent Eastern Bloc policies changed over time. When leaders first came to power in Moscow, they tended to announce that things were now different and that the Soviet Union would no longer interfere with the day to day business of its allies. Nikita Khrushchev and Leonid Brezhnev both argued as much, only to both famously call for an invasion of a Soviet shortly after (Hungary in 1956, Czechoslovakia in 1968). This is one reason that many in the West doubted that the reforms of Mikhail Gorbachev would lead to true independence in Eastern Europe, but when the Eastern European nations did start to rebel in 1989 he did not interfere as the Eastern Bloc fell apart.

Looking at the specifics of the pre-Gorbachev invasions, the evidence of the limits of Eastern Bloc independence, we can see that Eastern Bloc states did have the ability to set their own national policies to a great extent. First lets look at the key difference between the invasion of 1956 and the invasion of 1968: in 1956, Hungary attempted to leave the Warsaw Pact altogether, to not only set its own domestic policy but also its own foreign policy. The invasion, then, does not really indicate the extent to which an Eastern Bloc nation could set its own domestic policy. In 1968, Czechoslovakia had no intention of leaving the Warsaw Pact but in fact renewed its commitment to the pact and to the Communist movement in general, as its reformist leaders continued to provide war material to North Vietnam. Yet even still, domestic policy threatened the Soviets and the other Warsaw Pact leaders enough to warrant an invasion. Before we look at the reasons why, lets look at the Eastern Bloc of 1968 a little more generally, because it was not just Czechoslovakia that sought its own path.

The leader of Poland, Wlydyslaw Gomulka, was not a Soviet first choice. He had come to power during the tumultuous days of 1956. Prior to that, he had briefly led Poland after WWII, only be removed from power by Stalin and his closer allies. During the crisis of 1956, the Poles themselves chose to return him to power as a reformer who could bring stability to Poland. The Soviets yielded because he was in fact an anti-German Communist even if he sought to liberalize Poland in ways that made them uncomfortable. In 1968, he remained the leader of Poland, although he had ceased the reforms he had previously sought. Gomulka was already one example of domestic independence; had the Soviets been "pulling the strings" like many imagine, Gomulka would not have been chosen in 1956.

In Romania, the Communist leader Nicolae Ceausescu had been at odds with Moscow since well before Czechoslovakia's Prague Spring. He had ceased to participate in Warsaw Pact activities, though he never threatened to leave the pact altogether. In 1968 he even condemned the Warsaw Pact's invasion of Czechoslovakia. It is important to note, however, that Romania was not as strategically important as Czechoslovakia or Poland economically or geographically, so you view Ceausescu's stubbornness differently because Moscow did as well. In any case, Moscow certainly did not pull the strings in Romania.

Now on to Czechoslovakia and its Prague Spring of 1968, which led to the Warsaw Pact invasion Ceausescu condemned. Here we can see the full extent of Eastern Bloc independence (at least in the context of 1968) and where that independence ended. The Central Committee in Prague overthrew the Stalinist Novotny and elected the reformer Alexander Dubcek to power without interference from Moscow. Dubcek sought to implement massive economic and election reforms, and none of this bothered the Soviets much. Building on years of economic reform, this would have meant increased and eventually open trade with the West, as well as the introduction of a "profit motive" that would have allowed managers and workers to keep a large percent of their enterprises net profits. With election reform, Dubcek meant to allow the people of Czechoslovakia to play a more direct role in choosing their leaders and in designing domestic policy. Less famously, the Slovak Dubcek also sought to federalize Czechoslovakia and to allow the Slovak half a degree of autonomy, which obviously clashed with the Marxist-Leninist notion of the slow destruction of national identities. The Soviets were prepared to allow all of this. The problem arose with the lifting of censorship, as the rebellious writers of Prague began calling for the complete overthrow of Communist power not only in Czechoslovakia but in the Eastern Bloc generally. This sparked fears in the Soviet Union that in the absence of strict censorship Czechoslovakia would eventually leave the Warsaw Pact even if Dubcek was loyal to Moscow himself; moreover, it sparked fears throughout the Warsaw Pact that people in Hungary, in Poland, and perhaps even in the Soviet Union would soon demand that their own "Dubcek" came to power (a look at certain protest signs of the era reveals that indeed this literally happened). Dubcek continuously refused to reintroduce censorship no matter how hard the Soviet Union demanded it, and so Brezhnev eventually agreed with others that the Prague Spring should be put down by force. The knee-jerk reaction to this is to say "look how little independence the Eastern Bloc nations had!" A more nuanced analysis reveals that Czechoslovakia did in fact have an enormous amount of autonomy: it elected its own reformist leaders and put into practice their reforms. The Soviet Union only invaded after Czechoslovak initiatives threatened to undermine Soviet hegemony within the Eastern Bloc generally, and even then Brezhnev was strongly influenced by leaders in East Germany and Poland who feared they would be overthrown by their own domestic "Dubceks."

IN SHORT: No, the Soviet Union did not pull all the strings in Eastern Europe. Eastern Bloc nations had room for independent domestic policies. Moscow, however, would not allow these policies to threaten Soviet hegemony within the Eastern Bloc, and would use force to prevent a general collapse within Eastern Europe.

I have to point out that the concept "Eastern Europe" as it is used here was really a Cold War construct. Czechoslovakia was a "Central European" nation prior to the Cold War and that at one time meant something.