And, with respect to the desire for mechanics - while I understand the point in general, for this example it is not clearly relevant. As has been noted already, mechanical systems typically have the clause, "don't bother using the mechanics if success or failure is clear to you, the GM". The GM already ruled that the failure was clear.
IF the game had relevant mechanics, it would have been reasonable for the GM to not invoke them, and just jump to consequences. That's why I think the "...but, mechanics!" is a bit of a misdirection.
That leaves us with the more general question of "When and how do we pull PC's bacon out of the fire?"
You said in this post (the snipped part) that you think hawkeyefan missed the mark.
I don't agree. But I do think that you're missing the mark (with respect to what hawkeyefan has said) with the above.
Go back to his comment about "the Venn Diagram of consequences pertaining to what is realistic and what is interesting (meaning thematically compelling and/or provacative while simultaneously leaving what comes next up for grabs)."
What hawkeyefan is saying (and what I agree with and have advocated the same) is the following:
1) "Shades of mad tyrant" does not equal one singular response to any given stimuli or likely even be limited to a handful.
2) His personal guard, his court, his besieged people, and his militia/watch would not respond to a situation with one singular response or likely even be limited to a handful.
3) Humans (GMs) trying to model these interactions have blind spots. Worse still, they have to actually (a) convey all of the relevant situation and setting information that goes into both (1) and (2) above and have related the context of the overarching conditions to the PCs such that they make informed decision-points while (b) filtering that through their own blind spots, fatigue, and the fog and difficulty of recall inherent to multiple sessions.
4) As such, "going to the (player-facing) mechanics" and/or having strong, player-facing principles (perhaps those that aim toward interesting outcomes that follow from the fiction) to guide your adjudication of consequence gives you a pretty damn good chance of hitting that "realistic/interesting" overlap spot of the Venn Diagram. And (i) it reduces your cognitive workload in the effort so you stay relatively fresh after facing these moments repeatedly in a singular session. And (ii) the players are (broadly across a collection of many players) more apt understand the causal flow (with respect to both play principles, resolution procedures, and in-fiction dynamics) of action declaration > mechanical resolution > consequence.
I'm not convinced that this is a "player problem." Now that isn't to say I'm convinced that its a "GM problem" either. What I'm convinced of is, regardless of anything else, any action declaration in this situation of "I'm not cowing to this sonuvabitch that wields power ruthlessly and callously...I'm challenging him directly (and maybe his bark is worse than his bite, or his guard won't back his play, or the beleaguered people will rise up against him)" is a completely legitimate action declaration and "the player was bored" is an irrelevant value judgement (which I don't even know to be true, but that is besides the point). Its a thematically legitimate action declaration in D&D when faced with even Ancient Dragons, kings, let alone low tier lords/barons the like. The resolution processes, the setting, and the GM should be capable of absorbing that boldness and seeing what happens rather than just shutting it down. I mean, even if you're just doing Charisma (Intimidate) vs a DC 20 (with a 10 % chance of success...or a 10 % chance of success and a further 10 % chance of success with cost/complication if you're using that 5e module) to see if that is capable of revealing a Flaw (perhaps, "My Captain is becoming a mutinous bastard")...that is at least something. Personally, I think that any NPC that doesn't have some sort of interesting and diverse Ideal, Bond, Flaw composite that any PC can hook into to leverage for subsequent social interaction is very poorly designed.
With respect, a module with a pivotal NPC interaction that is nearly the social equivalent of the classic (and terribly dull) Anti-magic Zone block (to shut down the overpowered Mage's ability to circumvent an obstacle/challenge) in classic D&D exploration should be under the lens more and (if it were capable) have a bit more self-reflection.