So I know that the east german socialistic system would have NEVER been erected wouldn't the area have not been occupied by socialist troops. USSR first trained the political cadres. And later controlled them. It was their presence that backed their might. At the 17. June of 1953 it were russian tanks that squelched the uprising. Similar use happened e.g. in the "czech spring" and at other occurrences.
And still we all know that it was german people that executed this as well. From high profile ones like Ulbricht or Honecker or Mielke down to the polical commissars in the combinats. Germans.
And then we know that the east-german "Stasi" (secret political police) was blown out of proportion: they had 91015 members. Germans.
And we also know that the Stasi had lots of informations, IM "Informelle Mitarbeiter". 189000 in total. Germans.
So yes, my guess is that about 10% of the east german population was actively supporting the system. And this is not a singular meaning here, we all know that a good amount of germans suppressed germans. No one here is trying to shift it solely on the USSR. Not even members of the former SED (socialist union party).
I don't know where you've got the information about "always quick to blame", but I can say that for the FRG/GDR situation it is not really true.
As for your term "millions": that is actually true. Above I wrote about 198000 polical informations. But the SED (the socialist "union" party) had 2.1 million members. And then there were people members in the socialist "union" but not in the party. And so on... so yes, the support basis was quite high. This is why I assume that 10% actively supported the system (and, more or less, oppressed others). The GDR had 18.8 (1945) to 16.4 (1989) million people.