Agreed. I would frame it this way: there is authority over
backstory (histories, maps, cosmology, relationships, etc); over
situation (what is happening here and now); over
action declaration (which characters are doing what - this follows pretty naturally from
situation); and over
what happens as a consequence of the declared actions.
All these are parts of the shared fiction - the "narrative", if you like,
I think
@Ovinomancer and
@Campbell are correct to say that it is not true, in conventional D&D, that the GM has authority over all these things. An analysis of D&D that begins from the premise
the players do not have liberty to introduce any old backstory for free (eg the guards example in the OP) to try and conclude
the GM has authority over all of the fiction, including all backstory, all situation, and all outcomes, is in my view mistaken.
In 5e D&D, the players exercise some control over backstory via their PC backgrounds. These also influence situation - eg when a Folk Hero meets some peasants then the situation should typically be one of a friendly reception, unless the GM is just running roughshod over this aspect of PC build. How the declared actions are resolved in this sort of case seems like it is not under unilateral GM control either - given the player's contribution to backstory and situation, I would expect some reasonable degree of negotiation and/or consensus in action resolution (eg if the Folk Hero asks the peasants to hide the Macguffin in their haystack) or at least a relatively generous CHA-type check.
In AD&D, there were reaction and loyalty rules to resolve how a NPC responds if asked to do something by a PC. 5e doesn't have exactly those rules, but it does have rules for CHA checks. If a PC asks a NPC to do something, the default GM response in 5e D&D should be to frame an appropriate check. If the request is absurd - eg an out-of-the blue demand that the king relinquish his throne to the PC - then maybe no check is required. But how common are such absurd request? And of course if the request is not out-of-the-blue, or if the PC has leverage (ie is staging a coup or a revolution) then we're back in the terrain where a check seems warranted. (In the real world leaders forfeit their thrones from time-to-time in the fact of coups and revolutions.) GM authority over backstory and situation in these sorts of cases doesn't, as such, licence GM control over
what happens next.
In 5e D&D, it is almost always the GM who frames encounters with potentially hostile NPCs/creatures. And who draws the map etc in which these encounters take place. That is authority over backstory and situation. But once the swords are drawn and the spells start flying, the GM is not at liberty just to dictate outcomes.
What happens next, in 5e D&D combat, is governed by a host of rules (spread over the character build chapters, the equipment chapters, the spell chapters, the basic resolution/stat check chapter, as well as the stuff under the "Combat" heading). The GM is not at liberty just to ignore all that stuff.
@Ovinomancer has mentioned "secret notes" a few times. (I won't ask him where he picked up that analytical framework!) GM's secret notes work well, in typical D&D play, when they form parts of the backstory that the players, via their action declarations for their PCs, have to work out - secret doors that conceal secret passages, for instance; or the fact that the scullery maid is really the deposed former queen in disguise. Secret backstory might even include unhappy surprises that reveal themselves in the moment of action declaration -
there's an anti-magic zone here;
the ambassador is wearing a ring of mind-shielding;
this sort of aberration is immune to Domination;
there's another, invisible, foe who's about to attack your mage from behind for a boatload of damage; etc. But using secret backstory as a device for controlling outcomes seems weak to me, and a sign of poor GMing: examples like
this person will never give in to threats, no matter what they are;
this person will only provide the information if the PCs take steps A, B, C; or the notorious
if the PCs kill the BBEG, then NPC X, the second-in-command, fills the shoes of the deceased and keeps the pre-scripted events moving along.
This is the play mode that is typical of D&D modules from around the second half of the 1980s. There's no doubt a lot of people enjoy it. To the extent that it requires giving the GM control over all outcomes of action declarations, it does make something of a mockery of all those pages and pages of rules! - it did in the AD&D days, and still does in my view.
I can't speak for all the offspring, but in the case of Apocalypse World and Dungeon World this doesn't seem accurate to me. There are very few AW player-side moves that require the player to assert facts about the world or NPCs (the Battlebabe's Visions of Death is one, likewise the Operator's Reputation; and the Savvyhead's Bonefeel gives the player a degree of authority over situation). Seduce/Manipulate, on a 10+, permits a player to oblige the GM to have a NPC go along with the PC's request. The difference from a D&D CHA check is that the odds are clearl spelled out, and the restrictions on what the GM has the NPC say and do if the check succeeds are much clearer. But this is mostly about principles that govern the GM's narration - the GM has more constrained authority over the outcome than in the D&D case, but I don't think there is a fundamental cleavage here: the D&D GM's authority is just as constrained if a player's to hit and damage rolls oblige the GM to drop a NPC's hit points to zero.
AW does have the notion of
asking questions and building on the answers, so the GM can initiate or invite player contributions to backstory and situation. I'm not sure if that's what you have in mind?
That's where the clearest discussions are to be found of the different components of the fiction in a RPG, and how authority over them might be allocated in different ways.