If the player is just speaking for themselves out of character, what difference does it make in the game at all?
They can make suggestions to the GM about what they might find interesting. They can tell the GM what their goals and aspirations for their PCs are.
These are just examples from a longer list.
the core assumption of D&D is and always has been that the players are responsible for their PCs and what they do, the DM is responsible for pretty much everything else.
This is likewise true in Apocalypse World. From the rulebook (p 109):
Apocalypse World divvies the conversation up in a strict and pretty traditional way. The players’ job is to say what their characters say and undertake to do, first and exclusively; to say what their characters think, feel and remember, also exclusively; and to answer your questions about their characters’ lives and surroundings. Your job as MC is to say everything else: everything about the world, and what everyone in the whole damned world says and does except the players’ characters.
Differences in degree of player agency, in a RPG, can be created without changing the
subject matter that the different participants get to talk about. As per my post upthread, that I reposted at
@Micah Sweet's request,
in the RPGs I know that have higher player agency, the players cannot "alter game reality" in the way some posters in this thread are talking about. Rather, they establish their own goals and aspirations for their PCs (including working with the group collectively to establish the appropriate backstory and setting elements to underpin those goals and aspirations), and then the GM relies on those goals and aspirations as cues for their own narration of framing and consequence.
There may also be techniques that permit the players to declare actions or make decisions pertaining to their PCs' memories. This goes together with the players' establishing goals and aspirations, to overall produce characters that have "thicker" lives, relationships, etc than is typical of much D&D play.
What distinguishes (say) AD&D 2nd ed (as presented in its rulebooks) or
@Oofta's version of D&D as presented in this thread) from (say) AW or DW is not
the subject matter that the different participants get to talk about. Rather, in these approaches to D&D there is a core assumption that the GM is permitted to establish situations in which the PCs find themselves, and to establish consequences of what the PCs do in those situations, that are independent of the players' goals and aspirations for their PCs. This is the idea of the GM as a "neutral" referee, or as a presenter/narrator of the imaginary world that they have prepared in advance of actual play.