My GM often asks me what's what if-when anything maritime comes up - I grew up around boats and he doesn't really know a boat from a beachball - but he still retains full right of veto (rarely if ever exercised, but it's there nonetheless) if what I tell him doesn't mesh with what he's thinking.
The risk of allowing players to edit scenes are twofold. One you've already hit on yourself, that being a hard-to-manage increase in setting inconsistencies as things go along. The other is the risk of players editing scenes specifically in order to unduly benefit either their own PCs or the party as a whole; maybe not all the time (though I've known some who would) but at key pivotal moments, simply as an extension of the players' duty to advocate for their characters.
There's a lot of thought on this, albeit mostly from the Forge. To sum up in the most useful manner, you have a problem when a player of a game (regardless of role) has authority to decide both the challenge and the solution. This creates a state of play that isn't a game anymore, but it storytelling. It's also likely to be dissatisfying for the other players and even for the authoring player.
Game avoid this by having one player, usually the GM, present the challenge. The player tries to present the solution, which may or may not be subject to a resolution mechanic. This can allow a player to, indeed, "edit" a scene by authoring a success which, one would hope, will benefit their PC, but not unduly because of the constraint of the presented challenge and the constraint that the action address the challenge.
I think you may be thinking of a player declaring that they find 10k gold coins in the den of the kobolds, yes? That's usually not a valid action declaration because it doesn't follow from the established fiction -- ie, it's a non-sequitur. This is also a case of the player presenting the challenge (do I find 10k gold coins) and the solution (yup, in the kobold's den). It's not a valid action in the games I'm thinking of (although it would be valid in other games that are more storytelling exercises).
To give a concrete example, players in Blades in the Dark are encouraged to narrate actions such that they add to the scene. Like, say, you get in a bar fight and you grab a metal spittoon to hit someone with. The spittoon wasn't part of the GM's scene setting, but it makes sense that one could be in a bar. The GM either must let the action happen or can challenge it with the mechanics. Since this seems like it has the potential to make things more interesting, it should, according to the game principles, go to challenge. So, mechanics in Blades is such that it's heavily weighted towards success with cost or complication. Since the action is complex -- establishing a spittoon that within reach and that then is successfully used to hit someone -- the range of outcomes is pretty large. Let's say, though, that the action fails. The GM is now free to narrate that failure within the fiction established and the genre of the game -- ie it has to make sense. Let's further say that the GM had framed this opponent as armed with a knife. That means the fiction is likely to be dangerous to the PC. On a failure, the GM narrates that the spittoon is there, but it's slippery, and in the time it takes to get a hold of it, the PC is stabbed in the ribs, Harm 3 (this is bad, think sucking chest wound) (further, this would all flow from the resolution mechanics, part of which is a severity of failure component established before the roll). The player, though, still has lots of options. They decide to mark a box of armor, which costs 2 equipment, and reduce the harm by 1. They then use a Resistance roll (which costs stress) to deny the resolution, forcing the GM to reduce the impact again. The GM downgrades the Harm to 1, or minor, it's a nasty cut across the ribs, and it stings, but nothing that'll slow you down.
This example of play showcases the player editing the scene, especially at the end with the Resistance roll. The player forces the GM to mitigate the result of the failure, twice, but it still results in a good scene of play that doesn't unduly benefit the PC. This is one example of many kinds of ways games built to do this manage avoiding the kinds of situations you're concerned about.