I'm not sure what you think the force of the bolded can is here. Maybe there's some GM somewhere who makes those decisions based on a coin-toss. I don't think anyone would advocate that as good GMing, thoiugh. In this thread I'm not asserting that any rule was broken. I'm asserting that the system has ways to resolve the sort of action described in the OP, and that gameplay is likely to be better - more fun, more dynamic, with more player satisfaction - if those resolution mechanics are used.
I assert that may be so or it may not be. It depends.
As far as this particular case, given that - per the OP - the upshot was one player apologising to the GM for "ruining the campaign." I'm going to conjecture that everyone did not have a good time creating an exciting and memorable story.
Maybe, maybe not. Perhaps on the whole they did. Or maybe this one outcome ruined it. It's for the OP to say. You seem to be asserting that it is likely to have been better if they had just employed some Charisma checks. That is far from certain in my view even if I would have personally used the DMG's social interaction rules for this challenge. (And even if I did, there's no guarantee there'd be any ability checks either.)
And what you said didn't seem to add anything to what I had already posted in the thread. You quoted me saying "the GM is not - as best I can tell - expected to make that decision arbitrarily, or without having regard to the rest of the rules which (among other things) tell us what ability scores represent and what ability checks are for. . . . I don't see that it is good GMing to decide that a task is impossible when there is no reason in genre or logic for it to be so, and when - as appeared to happen in this case - it will create a less-than-satsifactory experience to so decide." Which bit of that do you disagree with? Clearly not the stuff on the right of the ellipsis, given that you have simply gone on to repeat it. The stuff on the left side? You think the GM is not meant to have regard to the rest of the rules, including what ability scores represent, in making decisions about whether or not a check should be called for?
What I did was point out some rules you left out, likely because you don't play D&D 5e to my knowledge and as a result don't read the D&D 5e DMG. Those rules state that the DM decides if something has an uncertain outcome, full stop. Tasks don't have an uncertain outcomes or meaningful consequences for failure by default. And if you're going to say there should have been some Charisma checks here and quote rules to make your case, you can't leave out the rules that say it's up to the DM to decide that if the task qualifies for a check. Not without making an argument that is full of holes.