@clearstream, I agree with
@AbdulAlhazred
You say "your friend concedes them authority over the ending of their book". But that just seems to conflate two things.
I mean, as a matter of fact the author is the author, and they are the one who decides what the content of their published (typed, handwritten, whatever) pages are.
But my friend can still imagine that the fiction is different, without any contradiction of any fact of the matter. She's not disputing (for instance) that JRRT has written that Fili and Kili are killed. She just prefers to imagine a story in which they were both injured and are now convalescing in the Iron Hills. And given that JRRT tells us little about Dwarven rules of inheritance, she can still imagine that those rules are such that the title passes to Dain, rather than to Thorin's sister-sons.
As AbdulAlhazred says, RPGing requires a shared imagined space, and so it creates a context in which each participant's imagination acts as some sort of constraint on the others'. This still doesn't give rise to objectivity.
It does suggest, though - and this is something that Vincent Baker has written about - that a process in which fiction is established, and becomes shared, and then generates downstream consequences for boxes and/or new clouds, will make that first bit of fiction seem more "real"/"objective" than one in which boxes go to boxes and the associated fiction is purely epiphenomenal.
For instance, suppose in Burning Wheel or Torchbearer, a player fails a Circles check. The GM decides to activate the "enmity clause" and introduce a new NPC into the scene, who is hostile to that player's PC. The GM asks the PC, "Why is this person angry at you", and the player gives an answer.
At that point, we have boxes (Circles roll) to boxes (GM activates enmity clause) to simultaneous cloud (GM narrates hostile NPC) and boxes (GM asks player to explain the NPC's anger towards their PC) to cloud (player's answer).
That final cloud - the player's explanation as to why the NPC is angry at their PC - is at this point purely epiphenomenal. And so cannot be expected to have a great deal of "objectivity" associated with it. But there are various devices, express and implied in both RPGs, for increasing the sense of externality.
First, both have rules for penalties to influence interactions between the PC and the "enmity clause" NPC. So if the player initiates social conflict, those rules will come into play, And if the GM is following the rules for narrating fiction associated with a social conflict, then during the course of the resolution process the NPC will be referring back to those previous events that underlie their anger at the PC. And so the player's answer takes on "external" force, being the precursor to further clouds associated with the various boxes of the social conflict resolution process. And of course some of those clouds will be ones introduced by the player, as part of their declaring of actions for their PC in response to what the NPC says in the social conflict.
Furthermore (and this is the implicit bit), the GM will be looking for ways to connect the player's explanation of the NPC's anger to other strands of the established fiction. (In AW, this would be the GM "misdirecting".) So already-established clouds get connected to new clouds by shared fictional explanations. This enmeshes the new fiction introduced by the player into a "network" of shared story that is not easily disentagnled.
These are ways in which the shared imagined space becomes enriched by new content, and that content becomes experienced as "external" and "objective". I don't think that narrational authority is especially crucial to this process, as opposed to a system that invites and requires lots of interconnections of fiction to be established. You can look at the rules for a system like BW and AW and see how this works. And conversely, a lot of the time when I see "player narrative control" criticised as ad hoc or producing thin or inconsistent fiction, I'm seeing processes of play that are not oriented towards establishing these sorts of interconnections. (Eg the player gets to declare that a guard at this gate is their friend; but there is no express or implicit process for linking that new cloud to other clouds, or boxes, that will enmesh into a network of fiction that cannot be "unpicked" and hence is experienced by all as a constraining SIS.)