Trust them to do what?
I've been a player for about 10 or so sessions in the past decade. I've GMed many more than that. When I GM, I don't want to be playing a storyteller/railroad game. Which is why I like systems that create structures and processes that don't require me to do that.
I posted an example oF what I want to avoid in the current "GM mistakes" thread: when GMing Rolemaster, the PCs had a powerful faction acting against them. I, as GM, had to decide how much effort the faction devoted to thwarting the PCs, and how seriously the resources dedicated to that effort were deployed. The rules of the game gave me measures for things like how many and how potent spells can a NPC cast, but nothing more. So all the rest was simply up to me to decide, with the upshot of my decision being the full gamut from the PCs experience little threat to the PCs are utterly hosed.
RM has no inherent devices for handling or mitigating this, because it's mechanics are basically more elaborate and simulationist versions of classic D&D mechanics (with a few exceptions - eg it has rudimentary but still workable social mechanics); but it assumes a completely different framing context from the very artificial environment of the classic D&D dungeon (which constrains and channels possible threats so the PCs don't get automatically hosed by the forces arrayed against them).
This experience is one reason why I prefer systems that - like classic D&D - provide a framework for the introduction and prosecution of adversity, but - unlike classic D&D - have a framework that will work in the more verisimilitudinous/naturalistic contexts that I prefer.
To give a concrete illustration of what I mean: in the most recent session of my Torchbearer 2e game, two PCs escaped from a prison in Wintershiven (the capital of the Theocracy of the Pale), abetted by a third PC. So there are now agents of the Pale who are hostile to them. But I don't, as GM, need to make any decisions in advance about who those agents are, how effective they are, etc - the sorts of decisions that I had to make in the RM game. Rather, the resolution system tells me (through various of its devices, like the rules for failed tests, the rules for events, etc) when I need to introduce "unanticipated" adversity, and there are also clear frameworks for establishing its difficulty, and there are clear frameworks for resolving conflicts (including clear rules for when PC death is on the line).
There is all the verisimilitude and vibrancy of my old RM game - I'm even using my same beloved 1980 Greyhawk Folio maps (though I think I actually got my copy in 1983 or perhaps early '84). But the game system improves the playability, by establishing clear procedures for the presentation and unfolding of PC-threatening adversity.
Talking about "trust in the GM" - as in, whether or not I trust myself (to do what?) - is a red herring.