Fair, I guess after 9/11, America is perfectly happy to show death on live TV. That is the "only way" the public will believe it happened after all.
As for USSR, I think if they did, they would have culturally lost out more. I don't know a whole lot about the cultural dynamics of the USSR, but from what I do know, I believe it would have hurt their psyche more as a unit to make themselves the object of ridicule. Think about it on a human to human perspective - Joe goes to the Moon, Sergei says Fuck off Joe, no you didn't. Joe says prove it. Sergei says well ___ and ___. Joe says TV says I went to the moon.
It makes the doubting party look like a clown. The USSR's whole construct was built on ego, much as North Korea's Juche is. Pure ego.
Look at what the Nork's believe - they believe that NK can cure cancer and aids, the Kim's don't need to shit or pee, disabilities don't exist, that KJU could drive a car at 3, that nature itself mourns the death of the previous leaders, that the NK's win every Olympics (they've spliced together videos to show people of their "wins") and my genuine personal favorite - that North Korea discovered real, true and honest Unicorns.
These aren't myths, the people truly believe those things.
Ego is vital for the survival. At the time, I don't believe USSR, if they thought that the moon landings were fake, would have said a single thing.
I don't really know what I think about the moon landings, but I do find what current astronauts (often the ISS ones) say about further space travel interesting. Maybe they just misspeak, but I do find it a bit strange that they've said things like "when we work out the Van Allen Belts and can go further than we are now" and things about going further out than the ISS orbit. Not solid proof, but its strange and I just can't logically chalk every time up to an astronaut misspeaking.