In Traveller (1977), when a player declares that their starship makes a jump, there are various throws to be made (to determine if a misjump occurs, if any drive fails, etc).
The GM is expected to narrate the consequences of those throws, but that is no different from how a D&D GM narrates the consequences of hp loss - and you are not including D&D combat within your "say 'yes'" rubric.
In Traveller (1977), if a player has their PC try and find a shady dealer, corrupt official etc then the rules specify what happens next: the GM sets a difficulty for the Streetwise throw, and the player makes a throw modified by their Streetwise skill. The GM has the job of setting the difficulty (by reference to the examples provided); but the player is not asking a question to which the GM might say "yes", any more than would be the case with
your giant rat example, where the GM has to set a difficulty for the attempt to shoot the rat with a crossbow.