I'll go with a fourth option - Possibly faked.
The cold war was still happening, there was a very real threat that the USA was going to go to war, then there was Fidel Castro (not sure of spelling) who was drumming up quite a bit of support against the USA.
America needed something positive to believe in again. And how to get all of America to be as one and believe in "the USA".
Such an undertaking required a few things coming together, such as a President who was well liked & charming and who was able to sell the idea of a science fiction to science fact undertaking!.
At the time it worked and did what it was designed to do, bring America together & say to the world we can and we have.
It's only now that the 'it was con' has gathered ground now we have technology to question the historical evidence.
Mind you I think in this day & age, we should be spending money getting this planet sorted out, let alone spending billions just to say let's have a go trying to get to Mars (not the choc) and let alone be let loose on another planet !!

PS. The Apolo Rocket had less computing power than a Sinclair Spectrum computer, think it was less than 3-4meg of computing power and was only to help with the early warning systems, not the main running of the Rockets systems. That was still down to the x3 Astronaughts and their slide rulers and pens.