It all depends on how it comes about that the PCs do not find any cultists at the teahouse.I never said that the game works is exactly like the real world. I said a GM telling a player who is at the tea house, when players say they are going there to look for members of Bone Breaker sect, is no more mother may I than if someone went somewhere looking for people in real life. I never said they followed the same process either. All I was saying is, like in real life, sometimes you go to a location to find someone and they are not there. That doesn’t sound at all like mother may I to me.
Here is one way: the GM decides. That is what, in the other thread, I have characterised as "Mother may I".
Here is another way: A check is made. If it fails, the GM narrates the consequence (which may include an absence of cultists at the teahouse); if it succeeds, the PCs find some cultists at the teahouse.
I think you think the difference between those two approaches is "pedantic". But there are whole RPGs and schools of play (Dungeon World, Burning Wheel and a common approach to 4e D&D among them) that are premised on adopting the second way rather than the first.
This is why I am not persuaded that you really appreciate the difference between "saying 'yes'" and "say 'yes' or roll the dice. Because every time you present a range of approaches, and talk about the role of GM judgement, and the like, you seem to disregard the possibility of "say 'yes' or roll the dice", even though that is very close to a standard alternative to GM-driven play,"Yes and" just allows anything the players want to unfold in the campaign.
<snip>
The GM instead of 'winging it' or saying 'yes' can think it through and try to come up with the most reasonable result to the question "what is there?"