If I am saying my characters does X how is that action not rooted in the fiction? I'm also not quite sure what a non-genre appropriate PC action looks like. Now I think you mean something more specific or nuanced by that statement but I can't tell what it is.
I'm sure there have been other replies to this by now, but I'll give mine. It will consist of a few examples.
(1) There is a big literature about "trying' in the philoso;hy of action and related areas of academic inquiry. For instance, most people woud say that a human being can't try and jump to the moon, because to
try means to have some sort of intention, and no one can genuinely form an intention to jump to the moon (as opposed to, say, jumping as high as s/he can) because everyone knows it literally cannot be done. (Maybe there are some people with radical cognitive problems who don't realise the moon can't be jumped to. Let's put them to one side, because in a RPG few if any people are playing PCs with such problems.)
This is why, upthread, I've referred to "genuine" or "sincere" action intentions, because I think action declaratoins like "I talk the dragon into giving me its treasure" are freuently going to be non-genuine or insincere. (That one is also ill-formed - it doesn't actually specify an action that the PC undertakes, it only describes an intention - but that's a further issue.)
(2) An example of a non-genre appropriate action declaration is given by Luke Crane in the Buring Wheel rulebook, when he mentions
searching for beam weaponry in the Duke's toilet as something that is impermissible. Likewise in a typical cowboy story
I try and outrun the horse is not genre-appropriate (whereas in a supers game it may well be).
One of the "problems" with high level D&D - which came up in your example of angels carrying someone across a gorge - is that the genre and hence the appropriateness of action declarations is often confused or at least uncertain. Cany the player of a high-level fighter declare
I swim through the lake for an hour like Beowulf did?
Under the broad label of "genre" we could also put action declarations that are contrary to the spirit of the game. Eg given the importance of treasure-acquisition in a lot of standard/traditional D&D play, action declarations like
I search the village well for a holy avenger will probably be inappropriate, and obviousluy so, and the GM can safely ignore or dismiss them. They are attempts to endrun around or completely ignore a basic premise of gameplay.
(3) That example leads into the idea of
action declarations that follow from the fiction. Of course if the PCs have been following a series of clues and defeating a series of opponents that have led them to the village well as the most likely hiding place of the holy avenger they need to defeat the whatever-it-is, then the above action declarations would
not be deviant or genre/premise-breaking. Because it would clearly follow from the fiction.
If you read through this thread you'll see that a lot of the "counter-examples" to a flexible/non-pre-scripted approach to adjudicating NPC responses - like dragons and merchants who give away their hoards at the first request - are ones that (a) violate genre/gamepay premise or (b) do not follow from the fiction or (c) both.
To finish this post, I'll give two examples from my own play that show how I use genre/premise and the fiction to "gateeep" action declarations:
(A) In my 4e D&D game, from time to time the players would declare that their PCs search a room for treasure, even though there was nothing to suggest that there might be treasure there. They were just engaging a FRPG reflex. Normally I would just tell them they find nothing; occasionally if I had something on my treasure parcel list that didn't already have a "place" in the unfolding fiction I might tell them they find it.
I never regarded this as very singificant - 4e D&D, with its treasure pacel system and as we played it - is not primarily a game of searching for treasure (cf, say, Moldvay Basic) and essentially random or ungrounded looking-for-treasure action declarations don't have to be taken seriously.
(B) In one of my Cortex+ Heroic Fantasy games, the PCs were lost in a dungeon after having been teleported away by a Crypt Thing (mechanically they were subject to a d12 Lost in the Dungeon complication). I described a chamber with strange runes (a Strange Runes scene distinction). One of the players had his PC read the runes, with the intention of seeing if they would tell him something about where he was in the dungeon. A successful check (that, mechanically, incorporated that scene disntction) established that they did indeed provide information about the dungeon, so he was able to eliminate the complication on his PC.
That's an example of an action declaration that followed from the fiction, and was appropriate to genre and to gameplay premise. If the game was classic D&D, it would be quite different - the GM would be expected to establish in advance what the meaning of the strange runes is, and recovering from being lost after Crypt Thing teleportation would be a dungeon-crawling-and-mapping challenge.