it is not a fake..do you not think the russians, who at the time wanted to wipe the yanks off of the face of the earth, who were in the race to get to the moon first would have spilt the beans if it was fake..?
they (along with us) tracked the whole mission using radio telescopes...the radio waves were being tracked from the rocket/shuttle and using the doppler effect it could determin the position within something like 10 meters...
there is no way the russians at the time or even now, would have kept quiet