There’s honor, and then there’s practicality
If anything goes wrong, the Director takes the bullet. If anything goes right, the Director thanks whoever did it. It’s unfair, but that’s the way it is, so if you’re the Director, suck it up and move on. Anyone who does it opposite comes across as an asshole and no one likes to work for assholes. Unless they pay a lot of money, but then it wouldn’t be a low budget movie.
This is not to say that fucking up on set gives you a free pass, of course. If somebody fucks up, the Director takes the bullet as a matter of honor, but I assure you everybody knows if there was a genuine fuckup, and it’s highly unlikely that person will be invited back to future sets.
I distinguish between fucking up and making an honest mistake. Everybody makes mistakes. Not correcting it is a fuckup.