First off, I want to assert that Vincent Baker's oft-quoted (including by me) "Say yes or roll" is NOT GM fiat.
Fiat is the GM stating that a conflict ends with a certain resolution. "Say yes or roll" is in fact arguing AGAINST fiat, by stating that rather than making a trivial unimportant question into a conflict, the entire issue should be sidestepped. No conflict, no resolution, no fiat.
That aside, I'd like to step away from the annoying tautologies and possibly ask a refine the question that I believe has arisen from this discussion -
From the perspective OF THE PARTICIPANTS, can mechanics be irrelevant? Can the be selectively irrelevant?
I believe they can be. Of course, I also don't think that every single thing that happens at the table arises out of mechanics. But in Halloween's excellent example of what I think we can all agree is an abnormal play group, the actual mechanics used to resolve in game actions were all handled behind the screen. The system could have been GURPS, or D&D whatever, or BRP, or FATE, or any number of systems, and from the players point of view it would be the same experience. I call that irrelevant.
We can argue about whether the verbal components of the social contract at the table count as mechanics, or implicit mechanics, or table rules, or whatever, but the die mechanics for that game were irrelevant to all but one of the participants.