We don't have the PHB, though, do we? We've agreed to play a game we don't have rules for. It's fine if we pick to play "as close to D&D as we remember and, if in doubt, Bob Says" but we cannot leverage actual rules to support the idea that absent the rules the GM must and should lead in all cases. You're starting from the premise that the GM retains these authorities merely because. Your thought experiment, though, doesn't support your conclusion that absent rules the GM is in charge. I don't think this is the foundation of D&D. Elsewise, the GM usurping PC control from players by citing rule zero is also just as much D&D.
Further, I think "rulings not rules" gets twisted out of intended shape. 5e rules are written to be loose and often require GM adjudication of the rule to fit the circumstance. This is the intent of rulings not rules. This gets twisted, though, when it's taken as the GM should just issue arbitrary or fiat rulings on outcomes when the rules exist for those things. Take Stealth as an example. The GM determines when you can hide is an example of the ruling part of this rule -- this is the GM's judgement. If the GM so decides, though, the rule this takes place -- DEX(stealth) vs WIS(perception), either active or passive as needed, and then the hidden rules. This is a rule that requires rulings -- there's not a rule for when you can hide, there's a ruling. But, once that happens, the rules do exist and rulings not rules don't remove those rules. That's Rule 0 territory, and is a separate thing. 5e does not give GM's carte blanche to do whatever with rulings not rules, and, I'd argue, not even with Rule 0 as this is to be deployed only in certain circumstances.
This is the bits where we get into GM Force, though. If the illusion is clearly what the player intends, and within the scope of their declaration, but the GM then negates this through other ways, like saying that this NPC wouldn't be fooled by such an illusion, then we're at the point that the GM is using Force -- they are forcing an outcome against established fictions. Do they have this authority? Questionable. I do not think that rule 0 is there to support this, and I don't think rulings not rules means that the GM should be subverting a rule used because they'd rather have it elsewise. And then there the bits where this kind of thing goes directly to the "trust" issues with regard to the GM.
But, all of this aside, the fact that the illusion exists is still narrative control by the player -- the illusion is there. If the GM chooses to subvert this by playing contrary to player intent for whatever reason they have, this doesn't remove the fact that the illusion exists.
I think that your argument also runs into even more problems if we step outside the long running quagmire of illusions and into Charm Person or Banishment or Wall of Stone. I mean, you can continue to pick examples that fall into those grey areas or negotiations that I mentioned in my post, but that doesn't remove the strong examples like these from still being there. In other words, my point isn't invalidated by an example that shows it incorrect -- it's only invalidated if there's a majority of such examples such that the point becomes an exception. I do not think you can make this case.
So why should there be trust blindly issued to GMs? Even good ones? I think I'm a pretty good GM, and I would not ever lean on "trust me" for anything in that role. I have to earn trust, even now with friends, because it takes very little to break trust. I have friends that I will play with but would never, ever let GM for me. They aren't breaking rule 0 when they game, either (I mean, how can you?), but I don't trust them to do the job. I'm sure others would be just fine in their games.