Players declare actions for their PCs. And say what their PCs think, and remember, and expect.
Those various actions rest upon an assumption about fictional position - what is "true" in the shared fiction, and how the PC relates to that "true" stuff.
The players' assumptions about fictional position will often include setting elements or ideas that have not been expressly stated by me as GM. When they declare their actions, those assumptions therefore get incorporated into the shared fiction.
Various examples have been posted by me, from 4e D&D and AD&D play.
@TwoSix also posted some examples, like "I punch the nearest guy" being declared by a player whose PC is in a tavern.
When I GM a RPG, the players are not obliged to ask me for permission or clarification before making assumptions about fictional position. And generally I don't want them to, for the same sorts of reasons as
@TwoSix set out way upthread: it makes for a bad play experience.