Lanefan
Victoria Rules
Well, no - sometimes it takes the form of "Dice, tell me how this turns out"....and it could be the player or GM or both who are saying/thinking this depending on the situation.This is very system dependent. In D&D, it's not generally true for the player of a magic-user or wizard declaring that s/he casts a spell, nor for the player of a fighter declaring that s/he draws his/her sword.
In Classic Traveller, if the players are playing a starship crew, and an accurate equipment list indicates that the starship is fully-fuelled, then the players don't need to ask the GM if it is possible to make a jump. They can declare the jump, and then the rules establish how to determine whether a misjump occurs, whether there is some other sort of engine failure, etc.
Many other examples, from a range of more-or-less well known systems, could be given. Or in other words, not all action resolution takes the form of "GM, tell me how this turns out."
The teahouse example (assuming little or no DM prep):
The player might ask her dice how good or successful her investigations are.
The GM might ask her dice what's possible to be found there (if anything) and then narrate the results if any based on both that and the player's roll(s).
In D&D, oftentimes a player whose PC is casting a spell needs to ask either her own dice or the DM's how it turns out, via an attack roll or a saving throw depending on edition.