I have checked out on this door exercise mostly, but I think the metagaming/unwarranted advantage situation is pretty clear.
Scenario: you describe how your character is searching the door for traps --- what your PC is inspecting, prodding, whatever, and then you look at me, the DM, expectingly, wanting an answer to what your character finds. I respond in one of the following ways (among other possibilities):
- I immediately look you dead in the eye and say "you find no traps".
- I look down at my notes for a moment, maybe turn a page or scroll on my laptop, nod, and say "you find no traps".
- I look at my notes, ask you to roll in the open, you roll high, and I say "you find no traps".
- I look at my notes, ask you to roll in the open, you roll low, and I say "you find no traps".
- I look at my notes, ask you for any searching bonuses you have, roll in secret for you, and say "you find no traps".
- I roll something behind the screen, maybe subconsciously (or consciously) mutter "interesting..." to myself, and say "you find no traps".
If you would have your character act differently --- does or doesn't follow the SOP, chooses to or not to open the door, asks another character to try because your character "sucks at this", whatever --- we have entered metagaming territory, because the same in-game reality has been established in all situations and yet something else, presumed to be our table process and out-of-game context, has influenced your decision.
I don't think it gets clearer than that. The severity, concern, and ramifications of metagaming are up to the table, but I don't think anyone could plausibly suggest that it didn't happen, unless you behave randomly/have your PC behave randomly, in which case the whole scenario was a waste of the DM's time (THIRD (sigh) EDIT: a waste of time other than potentially finding a trap, I will split the hair ahead of time, but a waste of time for evaluating no-trap-do-I-open-the-door next steps).
The problem with this observation-based decision is we can't test the 6+ options at each door to test that you have your character act consistently, branching reality style, so we have to derive the observations over many doors and see what they yield about your consistency. So inconsistent behavior --- "well sure, last time you did 1 and I opened the door without following the SOP but this time you did 6 and I had my expendable hireling open the door" --- raises an eyebrow.
Other than pointing that out, I have really lost track of what the trapped door scenario is supposed to be telling us.
EDIT: addendum: Lanefan rolls for the PCs to constrain the situations and dodge part of the potential for metagaming. Ditto for roll in the open DMs. Ditto for a DM just winging it. Those constraints can help both parties avoid metagaming, or lessen the "severity" of the "crime". Those are fine, if strictly personal preference, safeguards.
SECOND EDIT: I remember now (I seriously forgot) what this is supposed to be telling us: if the 6+ options and expectation for consistency mean we DMs are regulating what the character is "supposed to think". I don't think so, for a variety of reasons, because I care more about what the character does than what they think and because I think the door is a clearer cut game situation than a social encounter among those reasons.