Here is a simple opinion. I can believe that the Americans had some luck and landed once on the moon Apollo 12 and due to the low gravity got off again. What I cannot believe is that they managed to get it right so many times in a short period of time with the technology available.

The reason I am sure Apollo 12 landed is simple. They brought back parts of a previous mission and there are specifically placed mirrors on that part of the moon which are still being used today. There is no way they could have been mounted without being on the moon. Note they are used internationally and not just by the Americans. Furthermore, IF the Russians could have dismissed the American lunar landings as a hoax they would have done. Don't forget they had several missions which landed on the moon and returned to earth with samples albeit unmanned missions...