I was only 9 years old, but we were in the Soviet Union during Apollo 11's mission. The only thing the Soviets broadcast was footage of the capsule in the water and the hatch being blown. We saw the astronauts get out. The whole thing lasted maybe 4-6 minutes. I always thought that the only reason they showed that was because they thought there was a chance Collins, Armstrong and Aldrin were dead. My memory is that they acknowledged the landing and then dismissed it is as irrelevant. Something along the lines of, "The Americans have gone to the moon, but we are going to Mars!"
I personally never saw any US footage until A&E rebroadcast Cronkite's report on the 20th anniversary.
As far as the "conspiracy" of us not actually doing it, I've met people here who hold such.