What I think you're missing on the joke is that free speech in the USA makes it look like there's no propaganda, because of the plurality of opinions, media and propaganda.

And the Soviet has no conception of what that is - in his fantasy the US state, and all the "satellites" are controlled by one single narrative thread like in the USSR.

I think that's the actual punchline: he doesn't know what free speech is, so he thinks he's the one with the insight over the American.

The sad thing is that still echoes today in Russia, they tolerate a corrupt regime and cope saying "the others are also corrupt and filled with propaganda, so this is ok, at least we know, but they don't" not realizing there's no free speech.