I imagine they believe they could calculate the correct positions, but what would be stopping NASA from doing the same?

Nothing, of course. In addition to ignoring the fact that star positions are the same from the Moon as from the Earth, this claim debunks itself, since the ability of astronomers to determine if the star positions were wrong must mean that astronomer could tell what was right.

A variant of this claim is that NASA wouldn't have been able to portray the stars, regardless of positioning. I had a summer job as a planetarium operator once, and we were able to do that OK. Of course, we had a fancy Digistar projector, but the wonderful old bug-eyed monsters were accurately projecting stars decades before Apollo. It seems as if HBs have never set their collective foot inside a planetarium.

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