This depends on the table and their own rules honestly. In my DM’s table we go for a contested roll of deception/insight between our players or between NPCs. Now this might not be RAW, but we do it that way and we like it since it creates funny and interesting scenarios.
And for the RPG horror stories bit, I don’t think that if the DM is trying to force something that they’ll just obey the dice blindly if they aren’t in their favour. They’re just gonna turn around and say “oh no, you didn’t pass the DC / my NPC also has +30 to his persuasion, you lose.”
I mean, that’s why in any such contested roll between PCs you should have both parties agree to the roll and just see how the dice land? And if they don’t agree to it, they’re free to roleplay it how they wish to. That’s how we do it at least.
I don’t see why you have to call someone’s preference on how to play a “skill issue” though.