Worse, parallax of which stars?
Out of the top 20 or 30 brightest stars, only four manage to sneak in under 12 LY. Or taking it the other way, out of the first 50 nearest stars, only a half-dozen are in the low single digits for apparent magnitude.
And I'd think if, say, Alpha Centauri was three pixels to the left but everything else is undetectably different, that would be an easy fix.
Of course, the hoaxies start in all of their "no stars" discussions with a mental image of a star drop from Star Wars or similar; brilliant jewels (even brightly-colored ones, in some earlier flicks) on black velvet. This spectacle is behind the reason why they can never accept that the astronauts wouldn't spend half their surface hours looking up like someone at a fireworks show, going "ooh, ahh."
But even then...in their hazy simulation of thinking, they probably are going "millions of stars, way too many for anyone to edit in a picture." Far from. There's about 5,000 stars of visual magnitude, total, and you are going to have less than half of those visible at any given moment.
And as far as all the stars we are usually familiar with, and the ability of technical people to place them accurately in the sky relative to each other and appropriate for the time and location....have they ever even HEARD of planetariums? (Or planet-terrium, if you must). Which, until not all that long ago, had all of these precision placement done with hand tools.
