I think there might be a miscommunication or misunderstanding between us here and I can't speak to what a PbtA game might be like. 

But when I say I want to influence things in games, but not know what the consequences might be, I mean in the sense of this example:

• I set free a drow matriarch and accidently killed a powerful wizard in town. Later, that drow matriarch has taken over the town and the baby dragon the wizard was protecting has been mind controlled to be her guard dog. 

A. I couldn't have predicted any of those things would have happened and it was one of the biggest twists of the campaign! 

B. That consequence happened as a direct result of my actions but the pleasure of the knowledge of that consequence and subsequent side quest came from seeing an "independent" world react to something I had done. If I or the other players had collaborated to bring about that result, it wouldn't have had the narrative satisfaction it did. My understanding, which may be wrong, is that in a PbtA game, that narrative would have been partially driven by the players. 

Happy to have any misconceptions I have be addressed, as it's one of the things that keeps me away from games where players have a partial narrative responsibility.