Simply being human does not mean that there is always some small chance success. If the DM thinks that it makes more sense that there is no chance, then there is no chance. Other rules in the game are not relevant to that decision as such a decision is based on the DM's knowledge of the NPC.
I think the following, on p 2 of the Basic PDF, is relevant.:
Together, the DM and the players create an exciting story of bold adventurers who confront deadly perils. Sometimes an adventurer might come to a grisly end, torn apart by ferocious monsters or done in by a nefarious villain. Even so, the other adventurers can search for powerful magic to revive their fallen comrade or the player might choose to create a new character to carry on. The group might fail to complete an adventure successfully, but if everyone had a good time and created a memorable story, they all win.
I've bolded a couple of words that I think are especially salient. It is
everyone together who create a memorable and exciting story. It seems to me that that is highly relevant to a GM wondering what decision to make about what is and is not possible in relation to action resolution.
I further think that a GM who never permits a CHA check at any moment of crisis or confrontation, because s/he has always already pre-decided how an NPC might react, is not playing the game in the spirit that the Basic PDF presents.
To be honest I'm suprised that it's controversial to say these things. In AD&D it is well-known that there are better and worse ways to use the discretions that system confers on a GM. Eg there are better and worse approaches to dungeon design, better and worse ways to adjudicate action declarations, better and worse ways to award XP, etc. This is why we have notions like "killer dungeon" and "Monty Haul GM". It's true that both boundaries and particular examples might be controversial from time-to-time, but the general idea of standards of skill and quality is not disputed as far as I know.
I can't comment on 3E as I don't know it well enough, but 4e clearly establishes standards for better or worse GMing. The idea that it is not possible to apply any sort of standards or critical analysis to 5e GMing strikes me as very odd.
It may not be what you want to hear, but the DM can make the decision as to the uncertainty of the outcome or the existence of a meaningful consequence for failure by whatever means he or she wants. There is no roll except by the DM's leave. Different DMs will make different calls here and none would be wrong. Some calls may result in the group failing to achieve the goals of play - that is, everyone having a good time and creating an exciting, memorable story by playing - but we don't know that this is the case here.
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.
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.
Wrong? Maybe not, but better or worse? Sure, some of those DM calls will be better or worse, for a host of potential different reason. A lot depends on meeting the table expectations, maybe more than any particular opinion on example X or Y. If the DM makes a call that is in keeping with how play normally proceeds at the table he plays with, and is one that makes sense in terms of the pre-existing fictional context (i.e follows from the fiction) then it's probably a fine call, whether I personally agree with it or not. However, when the DM or the players depart from the table conventions things quickly start to unwind.
In pretty much every case the first litmus test I would use would be the question Does the ruling present interesting ways to move the fiction forward? If the answer is yes then the goals of play you list are probably being met. This does depend on the players buying in of course. One of things I don't really get about the situation in the OP is that several narrative lifelines were thrown to the PCs, with very little interest taken in them. That indexes a potential case of bad faith play, although without more specifics it is, as you say, hard to tell.
I am posting about what makes for better or worse GMing.
In this context I don't see any evidence for "bad faith" play - as I already posted upthread, if RPGing was full of people who turn up so they can flip over the table, that would be a sign of something pretty sad about the hobby. To me it seems like a player was frustrated and/or bored with the unfolding situation - perhaps in part because the fiction was not moving forward in a way that was interesting to him (? I think I saw that pronoun used). The player took a step to try and move things forward - "you're crazy and don't deserve leadership here" - which by all accounts of this module seems to be true, and uncontroversially true. The GM then escalated it to violence by having the NPC call for the guards, who turned up and sought to arrest the PCs.
I think this is the decision point that invites inquiry as to whether the GM made the best decision that was available. Reiterating that the GM didn't break any rule - as
@iserith and
@Maxperson are doing - doesn't seem to me to take that inquiry very far forward. Given that a player ended up apologising for "ruining the campaign", I think it's fair to infer that the ensuing episode of play was not experienced as satisfactory. I don't think that dissatisfaction is going to be resolved by just reiterating that the rules give a lot of discretion to the GM.
It appears you are more or less restating what I said after the word "wrong" in my last post.
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?
For example, I don't care how good a talker your PC is, you are not going to have a roll to persuade the merchant you just met to give you the contents of his store and warehouse for free. There is no other rule that has any bearing on that. It simply makes more sense that you have no chance to achieve such a nonsensical result, so you get no roll.
This is the sort of example I regard as compleltey unhelpful to discussion. Because it is not an example from actual play. It is not an example of an actual moment of conflict in an ongoing game where the players sincerely declare actions for their PCs.
The last time something like what you describe
actually came up in play for me, the situation was that the PCs (in a Traveller game) had taken a NPC and her ship and crew captive. The situation was tense and the PCs' control of it not total. The agreement reached was to gamble for ownership of the NPC's ship - the noble PC (a skilled gambler) against the ship owner (also a gambler). The player wond the dice-off, which is to say that the PC won the game, and title to the ship was handed over. The NPC now serves as a senior member of the crew on her former ship, with some other NPCs who were crew members under her command as well as other PCs.
Action resolution is how a game goes forward.