Do they need to break trust?
Because outright breaking trust with a single act is really quite hard. But doing something concerning? That's piss-easy.
And then to have your concerns met with some variation of:
1. Wow, I guess you just can't trust people, that must really suck for you
2. Don't you TRUST me, bro??? or
3. You should always trust everything the GM does, otherwise gaming is impossible
communicates that nobody is ever allowed, for any reason no matter how substantial, to ever feel concerned about anything, unless the DM so severely, so egregiously violates trust that the game is already over.
Except there are systems which make this quite doable. The assertion that it is utterly impossible is simply false.
How far does this logic go? Because Umbran's argument seems to work just as well here. Character dying isn't something players want to happen. It is almost always plausible that the character doesn't die from most threats which are at least theoretically lethal. That's where the "chunky salsa" rule comes from--if something happens that would reduce a character's cranium (or similar vital parts of their body) to proverbial chunky salsa, then the character is Just Dead. Things short of that standard, survival is still in the range that makes sense.
So why is it okay to have rules which tell you your character just dies, but not okay to have rules which (say) tell you your character thought they knew what they were doing better than they actually did? Both of those are entirely real-world events, and the latter is (thankfully!) much more common than the former.
Why is it okay to have rules which tell you your character flubbed their attempt to convince a shopkeeper to cut them a deal, but not okay to have rules which tell you your character flubbed their attempt to adhere to their (entirely mundane) oath against consuming intoxicants?
Why is it okay to have rules which tell you that your character's ability to tell if someone lied to them failed when they really needed it, but not okay to have rules which tell you that your character's courage failed when they really needed it?
All of these situations seem to follow the same exact logic, but the former is somehow acceptable because...it was what games did in the past, while the latter is unacceptable because past games didn't? I don't see why "when in Earth history this mechanic first appeared" makes any difference in the degree or nature of agency loss to these mechanics.