Not exactly. There were problems with the official film of the Moon landing. Nobody knows whether this was because the quality was such that you couldn't tell what it was or (here the conspiracy theorists are having a ball) whether there were things on the film that were considered not for the public's eye.
The film commonly seen was shot in Stanley Kubrik's studio with Kubrik himself taking control (he did a deal with the 'powers-that-be' but nobody knows exactly what - there are documentaries on this subject readily available) of some scenes.
So yes, we did land on the Moon but most of the film was re-shot.
Do they allow to roam around unsupervised or to vote in Australia?