You don't SEE any pictures of them on the moon, per se. You see a bunch of spacesuits walking around on a rocky, grey, poorly lit surface. You're told it's the moon. You're told it's the crew of that particular ship. It's not like you can see any faces.
And many of the prior lunar launches came within very close range of the moon. They usually couldn't slow themselves enough to be able to land the module, launch it, and catch it. Remember, the rocket itself never actually touches the moon. Those things are designed to be disposable. Also, sometimes, there were technical glitches. Most of the early attempts at the moon were *painfully* close to success. Aside the ones that were called off on account of weather or whatnot.
So, the missions follow this plan: launch rocket, achieve orbit around moon, drop module in general landing area, walk about on moon, launch pod that comes with module, catch pod with shuttle, go back to earth, and crash-land in the ocean. If the module cannot safely land and be retrieved, you give up and go home. Then, when they pick everyone up, they take what they can back with them and leave the trash to sink into the depths of the sea.
The only change you need to make is *really* simple: bring along a taped fake of a lunar walk. Quite probably, the voice-over was done on earth, by the astronauts. It's not like you have to worry about audio slips... just use the actual com. radios of the suits themselves. And a simple enough order: if you can, land on the moon. If you can't, use the fake. We probably won't have another shot of this within the deadline, and the american people need this victory. Good luck.
And then, the very next launch happens ahead of schedual (or, at least, not behind schedual like all the others). And everything goes so perfectly, and they manage a moon landing. Making the fake unnecessary, but it's not like the guys in charge could go. "Oh, the first was a fake". And until the crew of that first launch are dead, any person who knows is going to keep quiet to protect them.
