It is more about trusting the population at that time. Today people are incompetent and dishonest. At that time, it was the opposite. People were generally competent and honest. This means that they were capable of going to the moon, and that lying on a large scale was impossible. Lies like the Watergate scandal and various lies about Vietnam were all exposed. The media was fairly honest. So faking something like the moon landings would have been impossible.