I am not a biggest fan of this. Now some extrapolation based on character background is pretty much fine. Like a player deciding in middle of the session what the character's favourite bar is like can be seen just really being about the character; the player should be able to define in what sort of place the character likes to hand around, and that tells us something about what sort of person they are.
But this approach often takes things beyond that, and when the players are asked to provide facts about the world not related to the character, I think we are firmly in the players being part-time GMs territory.
And despite what Alexandrian thinks, this is not automatically bad, but what he is corrects about that this simply is not what some players want from being a player in a RPG.
Personally, as player I can do it and I can do it well. It is not about that. But frankly, I rather not. It takes me out of being the character into the writers' room, being a co-GM. And I already GM a lot (and I like it) but ultimately when I'm a player I am looking for something completely different than I look for from GMing. It is not the worst, I am willing to play a game this way from time to time, but I will never be my favourite either.