Brief note: I do believe that the moon landing happened.
I'm seeing this argument a lot here on Reddit that this is the biggest reason they believe that the moon landing happened is because the Russians didn't question it. I personally wouldn't view that as a solid argument unless the Russians knew more about the moon landing than what Americans had been told/had knowledge of, since then it would really just be us saying because one group of people believed something with the same information we had then we should believe it, too.
Thanks for any responses.
There were numerous independent optical and radar tracking observations from around the world by amateurs and academic sources. Soviet technology was at least as good as amateur technology, and considering they'd already sent interplanetary probes to Venus, it's safe to assume they'd have their own observations to compare with international sightings.