I think there is room for nuance here.
For instance, as a result of something that happens in play Kim is able to tell Tran some of Tran's character's desires/motivations. (Eg by imposing a fear effect or condition.) Tran still gets to declare their PC's actions, but doesn't get to decide everything that their PC feels.
Even in the ordinary case, when the GM is telling the players what their PCs see and hear, the players are, consequently, not deciding
everything that their PCs think (eg the GM is the one who decides that the PC thinks
I can see a door about twenty feet in front of me).
Another possibility I know arises in 4e D&D, and in principle could arise in 5e D&D.
Suppose a fear effect causes a character to move (ie recoil in horror/terror; in 4e I'm thinking of the Deathlock Wight) or to be paralysed with fear (in 4e this is represented via the stunned condition). The player may have a resource that permits them to respond, either when the effect is first imposed, or at some subsequent point (eg if making a saving throw vs stun): in 4e this would probably be an immediate interrupt or a "no action" ability, while in 5e it would probably be a reaction. The player deciding whether or not to use this ability is, in my mind, clearly playing the game even though they are not, at the point of making that decision, deciding what it is that their PC thinks or feels.
I think clearstream's point turns on more than just inadequate GM narration.
Let's start with the low-hanging fruit: suppose that, in the fiction, there is a trompe-l'oiel effect in place - from a painting, or in D&D more likely from illusion magic - and it is established (using some or other process - eg the player has looked at a GM's handed out illustration; or has failed to "disbelieve" an illusion; or has not used a Detect Magic effect even though they are in hot pursuit of an illusionist) that a PC is fooled by it. The player declares
I walk down the corridor - but the GM's response has to be something along the lines of
No you don't - there is no corridor!
Another version might be a stone carving or ceramic structure painted and polished to look like wood. The player declares
I set it alight with my torch and then discovers, again via GM narration, that it is not flammable.
One-way or locked doors are another D&D staple for this: the GM responds to
I open the door with
You can't open it.
The general point is that, in typical D&D play, players learn the GM's conception of the setting primarily by declaring actions and receiving GM narration in response, and some of that narration is explaining why declared actions fail.
And the more general reason that (in my view) sits behind
@clearstream's point is one I posted about a couple of years ago:
Players choose what their PCs do . . .
Every action is amenable to more than one description: in the example I gave in that thread, taken from the philosopher of action Donald Davidson, "I flip the switch, turn on the light, and illuminate the room. Unbeknownst to me I also alert a prowler to the fact that I am home. Here I need not have done four things, but only one, of which four descriptions have been given."
If a player proffers a description that contradicts some hitherto-unrevealed aspect of the fiction, which the GM then draws on to establish what happens, the GM is going to veto the player's proffered description and put forward a different one that avoids the contradiction: so instead of
I open the door the GM puts forward the "closest" (not a technical term)
true description in the neighbourhood:
You grab the door handle and push and pull, but it won't open!
Or in
@Lanefan's example,
You start to scan and feel the wall closely, looking for holds and a path up, but it looks like it probably can't be climbed or maybe even - if this is consequent on a failed climbing check, for those versions of the game that use them (the Basic PDF, p 64, flags that "At the DM’s option, climbing a slippery vertical surface or one with few handholds requires a successful Strength (Athletics) check) -
You scan and feel the wall closely, but you can't find any holds sufficient to climb it - it's too steep and slippery.
For what it's worth, I prefer an approach where the players declare their actions
without the "try" or "attempt" - which I find a bit irritating or insipid - and then the GM corrects with the true description where the player's proffered description can't be true.
Intent and task makes me think straight away of Burning Wheel, which - to the best of my knowledge - is the RPG that coined the phrase to describe it's approach to action declaration and resolution.
In BW the declared task is purely hypothetical or aspirational, in that we don't know whether or not it was achieved until the outcome is determined. If the declared action succeeds, then both intent and task are achieved. If the declared action fails, then the GM narrates the failure, with primary attention paid to the intent but with the option to also narrate some degree of failure of the task.
But a crucial element of BW, that accompanies
intent and task, is
say 'yes' or roll the dice: ie if there is nothing narratively at stake the GM says yes, and otherwise the dice are rolled and from that either it follows that both intent and task succeeded (if the player succeeds on the check) or that intent was not achieved, and perhaps not the task either (if the player fails the check).
I think in 5e it is more complicated because it is possible for the task to succeed yet the intent fail, due to considerations recorded in the GM's notes; and it is possible for the GM to say "yes" or to say "no" based on adjudication of the fiction rather than having regard to narrative stakes or the outcome of a check. So we can't treat the player's declaration as purely hypothetical pending a roll of the dice - because not all action declarations trigger a dice roll even if there are genuine narrative stakes - but nor can we always treat the player's description of their action as in-principle feasible (because it may be contradicted by as-yet unrevealed stuff in the GM's notes).
Hence why I prefer the approach I described earlier in this post - the player declares their action without the language of try/attempt, but the GM corrects the description if that is what is necessary to achieve a true description of the action relative to the fiction including the as-yet unrevealed fiction.