'In a city, people are talking' is rather logical assumption, some might even say it is self evident and it would indeed be weird for the GM to rule that this is not the case. (They still could, but unless there was some really good reason for it, it would be terrible GMing.) Similarly it is practically automatic that a city would have some rumours and local goings on as that simply is a part of definition of city. But again what exactly those things are is for the GM to decide.
And you continue your obfuscation of who decides what. In normal 5e D&D it is not assumed that a player can invent a a thing and then declare that they seek information about that thing and this act causing the thing or even the information to exist. If a player just invents a Lich Queen and their crown and declare that they are seeking information about it, the GM is fully within their rights to declare that the character finds out nothing, because the Lich Queen and their crown simply are not things that exist. And even if it was established that they exist, the player cannot just declare that they investigate whether the crown is hidden in any location they happen to be in, and the success causing the crown to appear there.
EDIT:
Also, I thought you originally argued that Burning Wheel has greater player agency than D&D based its different mechanics yet now you seem to be arguing the D&D actually works similarly so I really have no idea what you're even arguing about...