You're certainly correct about the 'uncomfortable viewing' the press conference makes but I suspect that could easily be attributed to tensions within the astronaut group themselves, the reluctance of men trained to work in isolated circumstances having to face a roomful of combative press from around the globe and also the simple fact that they were a long way from their own comfort zones. These were men used to being in charge and working to strictly defined parameters; facing the press can't have been easy or indeed even manageable. But I think you put your finger on it when you observed:
Anyone who feels that governments are not capable of such vast cover ups needs to look at .,.. the Manhattan project
but the Manhattan project itself leaked like a sieve, with Karl Fuchs being the lead leaker. And surely that's the point, isn't it? If something as big and as serious as the creation of Nuclear Weapons can't be kept secret, when entire organisations were created for specifically that purpose, how is anyone expected to believe that a comparatively open and straightforward project such as sending people to the moon for a couple of hours was in reality the imaginative project of a few cunning tricksters who managed to pull off the greatest con-trick of all time, and leave not one solid, indisputable piece of evidence?