If the FT starts with A and B in the wrong spots then, yes, the officials (all of them) have messed up.
BUT, you don't screw things up further by ignoring the proper way - per rule - to deal with the situation. It's the same as having 6 players on the court. You can't just stop play, say "oops" and have a do-over. The coaches and players have some responsibility to follow the rules, even when they're not perfectly enforced.