There are two interpretations of this.
One is fairly trivial: the GM handles the backstory, the players declare actions for their PCs. Most RPGs works this way. Apocalypse World, Tunnels & Trolls, RuneQuest, Burning Wheel, the Dragonlance modules for AD&D - they all work this way.
The other is false: if a player declares
I open the safe to look for the documents, and the GM's notes have determined that the safe is empty, then one true description of what the character is doing is
opening the safe that doesn't have what they want in it. And it is the GM who has decided that that description is true, in virtue of their authoring of their notes, not the player.
The only person entertaining that idea is you. I'm not.
@Campbell is not. We are talking about
who establishes what is at stake in an action declaration, and
whether or not an action declaration resolves a situation. The fact that a player can decide their PC wants to look for some documents in a safe tells us nothing about the things Campbell and I are talking about. We're talking about
what happens next - how is it established (i) whether or not the PC opens the safe and (ii) if they do, what they find in there, and (iii) whether or not they open it, and whatever they find, whether some further consequence results.
I've already given one example in this thread where they do: the Knock spell gets in the way of resolving the opening of a safe to try and find documents in a conflict resolution fashion.