I don't disagree that telling stories is amongst the several functions of tabletop RPGs (though it's certainly not the only function, or even the principal function of many games), but I think a lot of analyses of story-in-RPGs trip over the GNS model's error of treating the activities of play as identical with the goals of play.
Like, if the goal if play is to produce a story, then the act of play must be identical with the act of telling a story, right? Except that's not how most stories we actually tell work. How most stories we actually tell work is a bunch of Weird Shit happens, then we make up an explanatory narrative to help us make sense of it.
In the overwhelming majority of conventionally structured tabletop RPGs, the act of play is not identical with telling the story. The act of play is identical with experiencing the Weird Shit. The rules are a Rube Goldberg machine which outputs the materials of which stories are made, and if they're competently structured, all you need to do is turn the crank.
This, more than anything else, is why putting Rule Zero front and centre is going to give you problems in traditional games. If you start with the exact specific story you want to produce and ask how to get the rules to produce it, you're not merely setting yourself at odds with any particular rule; you're trying to run the machine backwards!
