I'm not talking about who invented a setting element. Presumably Gary Gygax invented Nyrond (in the narrowest of "invent"), although to the extent that it is really just a stand-in for Aquilonia or some similar Hyborian kingdom then REH invented it, and to the extent that it is really just generic pseudo-historical mediaeval kingdom #101, then no one invented it - it's an obvious sort of thing to include in a fantasy setting.
I'm talking about
who actually makes some fiction the focus of the action.
Who wrote the setting? Suppose that the GM established the setting
detail, who called for that sort of thing to be part of the setting?
An example, based on something from a long time ago when I was GMing Rolemaster: a player wrote up his magic-using PC, and as part of his backstory had a mentor who (i) lived in a giant hollow oak tree outside the PC's home village of Five Oak, and (ii) was hiding there from powerful enemies in Nyrond. Five Oak and Nyrond are both places on World of Greyhawk maps. The player, being familiar with the maps, made the backstory decisions that incorporated those places. What
Five Oak "means" is
a reasonably small village in a forest not too far from the City of Greyhawk. What Nyrond "means" is
a large, important but threatened kingdom some distance from the City of Greyhawk.
At some later point in play, I 9as GM) introduced a situation in which the mentor was missing, and there were obvious signs of disturbance/assault in his oak tree dwelling. The player's (and players') attention naturally turns to powerful enemies in Nyrond.
From what I've said so far, I think it's an open possibility whether we're talking about the GM or the player generating the fiction that is the focus of play. It seems to me to depend on
what happens next at the table. If the GM uses the kidnapping of the mentor as the hook to have the players play through an adventure the GM has designed - say, some variant of the slave lords or similar scenario involving multiple sessions of play in which the PCs, piece by piece, dismantle and defeat an evil organisation - and the players' decision-making is predominantly tactical or instrumental decisions about how to do that, I wouldn't say there is a lot of player-generated fiction in respect of the focus of play.
On the other hand, if the kidnapping of the mentor leads into a series of situations in which the player's decision-making does contain a significant element of
making decisions about stuff the players have flagged or otherwise rendered salient - eg their are choices about alliance with or opposition to other NPCs with meaningful relationships to the PCs (as established via flags and/or prior play) - and the status of the mentor and the powerful enemies and how these relate to the PC are all front-and-centre not just as hooks but as the actual subject-matter of play and decision-making as events unfold, then there probably is quite a bit of player-generated fiction in respect of the focus of play.
To reiterate: one of the sorts of player-generated fiction I identified in the OP is
player-generated fiction that pertains to the focus of the action. That is, the player deciding what "the story" is about. (I use scare quotes because "story" is a contentious term in the context of RPGing.)
This is why I think
@FrogReaver's examples of GM-presented options, choosing modules etc are really not all that on point. Suppose that the players decide to follow the GM's lead of "investigating an ancient fortress". During - let's say - 7 hours of play, a lot of fiction will be created. A lot of words will be said. This fiction and those words will have something that they are about. And I'm discussing
who it is that generates that.
So, in my example upthread of 4e play, a significant episode of play involved talking about soul energy, and whether Vecna or the Raven Queen was going to have it, and why it is bad that Torog currently has it, and how it might be redirected, and so on. It was the players who generated much of that focus.
On the other hand, the most recent time that I GMed AD&D we played a session of White Plume Mountain. There was a lot of discussion about pit traps, and the heat induction trap, and the ghouls, and the frictionless surface pits, and so on. It was me as GM, mediating the module, that generated much of that focus.
The proposition stated in the previous paragraph wouldn't change if the players, playing their PCs, had "diegetically" followed up on a possible plot hook about recovering stolen weapons from Keraptis. Because even if in some notional sense the players (as their PCs) had chosen the goal of recovering weapons, the actual focus of the action would still be al this stuff coming from the module and mediated by the GM