The rule itself is not saying that you the player are the one who can declare fiction, though.
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3) The DM narrates the result of the adventurers' actions.
This, right here, is the crux of
@pemerton 's thesis. The problem is that "GM narrates results" is NOT ACTUALLY WHAT HAPPENS.
What actually happens is, "The GM makes a follow on proposal upon which the group must either agree or negotiate the resolution before play can continue."
The fact that the vast majority of time that there's no active negotiation doesn't remove that step from the process. If the players instantly, silently agree, they've still made an evaluation---they see that no negotiation is needed, and make an active choice of agreement.
@pemerton 's point is that all rules exist to serve a purpose in that negotiation phase prior to agreement.
In combat, it's to ease the negotiation between, "your character took 18 hit points of damage," and "your character is dead." As a GM, though, I can at any time unilaterally declare "your character is dead." But I'd better be prepared for the negotiation to follow if that declaration was made unmediated by rule.
The vast majority of rules, though, are PC/DM neutral and are not about who determines what is happening in the fiction
Well, yes, I suppose, if you mean that ultimately there must be some arbitration of what is true, and that it's assumed the arbitration is usually handled by a single person. A game that states that the GM has final authority on determining the "truthiness" of declarations is making a broad assumption that can be misleading. Full group assent is required of the fictional state truthiness, no matter what the rules say.
There's never going to be a rule that states precisely who introduces what, when. The rules are for the mediative act. If only one party can introduce truth to the fiction, there's no need for rules to intermediate.