5e lacks any particular vehicle by which a check result can be made binding on a GM, nor any specific 'valence' which can be assigned to it, so there is IN ACTUALITY no such thing in 5e as resolving something by a check! A GM may, at his pleasure, decide to ask a player to make a check, and then he may or may not attach some significance to the outcome. It is literally no more binding than the way some GMs idly roll dice themselves and decide what to narrate based on the results, or things like reaction checks in 1e AD&D where the GM might (or might not) roll some dice and apply some, all, or none, of various modifiers and then narrate something.
The funny part is, once you look at it this way, the OP is kind of wrong, really, the RULES don't actually hold the GM to giving them ANY input into how things play out. Only the convention that D&D is a game, and the presumed desire of players to actually participate in an active way gives them authority (and this is a weighty factor, make no mistake). The thing is, once we get here, where's the remaining 'game' in the OP's apparent hypothesis? The reality is that 'rules' are not even a part of it, at least in this paradigm, its purely a social matter. Now, if you play some other types of games, at least the rules do say "and you, GM can do THIS, but not THAT, and you MUST do this other thing." That more clearly distinguishes "you are playing this game" from "you are making up something but it isn't an instance of Game X." We might look at this as a deliberate feature of 5e, it is really impossible to say if you are or are not playing a game like 5e. This is the sense in which it is a 'big tent' (assuming you can say it is, but lets not go there) nobody is NOT playing it, heck, even if they're playing tiddlywinks!