I think that what's happening in play as described is the GM has crafted a setting for the players to interact with.
I find the language of "interaction with the setting" tends to obscure what is going on.
The players interact with the GM. By saying things. Perhaps also pointing to things - eg "We go <here> on the map."
The GM interacts with the players by saying things, showing them maps, showing them pictures, etc.
The setting tends to used, somewhat indifferently, to refer to two things that are related but not identical:
(A) An abstract object - namely, some collection of descriptions, ideas, etc that collectively constitute an imaginary world (eg all the ideas that JRRT came up with that, taken collectively, constitute Middle Earth);
(B) A collection of more concrete things - writings, pictures, beliefs/thoughts in the GM's head - that, collectively, (i) encode/express bits of (A), and (ii) serve as cues or aides memoire or resources for the GM to make decisions in the course of play
When we talk about
the players interacting with the setting, what we mean - I think - is something like:
* The players have some beliefs/thoughts that encode bits of (A) - stuff the GM told them, stuff they read from the blurb on the back of a book, stuff they've picked up from their own more intensive reading and/or listening, etc.
* Using those beliefs and thoughts to help inform their sense of fictional position, the players declare actions for their PCs.
* The GM, drawing on (B) above, makes a decision about what happens next - or decides to disclaim decision-making to some extent, and makes a dice roll of some sort or calls for a player to make a roll of some sort.
* The GM relays some of that decision to the players - not necessarily all of it, as the GM may make decisions that add to or change (B), which the GM doesn't share with the players (consider, eg, the example where, by charming a NPC in a tavern, the PCs bring it about that the duke is not protected from assassination).
It could probably be unpacked a bit more, but I think what I've said gets at the general gist of it.
As for whether authority and control are established fact, I think in many... likely even most... cases, they are.
I disagree a bit about how much authority you have as a player in D&D. You likely have a little bit over the world (assuming some amount of GM leeway) in the form of backstory or details about your character... NPC friends and families and the like.
You likely don't have 100% authority over your character in the sense that you are bound by the constraints placed on you during play. You can't necessarily "go anywhere" since the GM can block your means in any number of ways. Want to travel to the north port? Oh, sorry... weather prevents it. Want to enter the southern kingdom? Oh sorry a magical barrier created by the god of thwarting surrounds the kingdom. And so on.
This is why I think the amount of GM authority matters quite a bit... it impacts play quite a bit. It determines what is available and what the players are allowed to do.
In my more recent posts, I've been distinguishing authority and control, using chess and bridge as my examples.
In chess, a player always has authority to move their pieces. But the rules of the game and the position of the board constrain and guide how they can exercise that authority. And the way that a player wins a game of chess is to make their own moves so as to exercise
control - increasing control, as they proceed towards victory - over the position and the "possibility space", constraining and guiding the other player's exercise of their authority, until there are no options open to the other player.
The losing player does not forfeit their authority over their pieces on the board. But they do lose control of the game.
Bridge is the same. Players (other than the dummy) have authority over the play of their guards. But their are rules that govern them - the most important being the requirement to follow suit. And the skill of playing bridge is to use
your authority so as to control - constrain, and guide - the way that other players use
their authority (eg by exploiting strength and length to run other players out of trumps, and then win further tricks in off suit).
We can analyse RPG play in much the same way.
For instance, consider a simple example I gave upthread, which could be part of dungeoncrawl play:
GM: you're standing at one end of a hall.
Player: I walk down the hall.
GM: You fall down a pit trap.
Here, we have the GM referring to their map-anbd-key to tell the player what the PC sees; the player declares their PC's action; the GM refers to their map-and-key to determine the consequence.
The player (or perhaps another player who has a PC who has seen what happened) now has more information, and so can do things like the following:
Player: I lay a board across the pit, and cross the pit on the board.
Now the GM is constrained, by the logic of the new fiction the player has created. The GM is obliged to agree that, in the fiction, the PC has got to the other side of the pit safely.
And perhaps the player goes on:
As I walk down the hall, I prod in front of me with a sturdy wooden pole.
Now, the GM is obliged - by reference to their map-and-key - to narrate the PC triggering pit traps by use of the pole. Thus providing the player with information, which allows the player to declare more actions like laying down boards, moving around the edge of revealed pits, or whatever.
In addition to the precise analysis, the other thing I'm trying to get at is that the player can exercise control over the shared fiction
without having to enjoy authority over it. Just like a chess or bridge player, they can make moves that constrain and guide the moves open to other participants, by exploiting rules and position (in the examples I've given, the rules include things like
the GM is bound by their map-and-key and
everyone agrees that common-sense logic for dealing with pit traps will work).
The less bound the GM is, and the more baroque the rules and the position, then the harder it becomes for the players to exercise control. The example of the NPC whose role is such that if the players charm her as she hangs out in the tavern, the duke will be assassinated, is in my view a pretty baroque position that relies on very permissive rules about what the GM can extrapolate to. Likewise, I would say, the example of guards not being able to be bribed because of their periodic interrogation under a Zone of Truth spell.
