I don't really see how this follows. There's no element of that principle which talks about players vs GMs. All that is required here for collective storytelling is a split of responsibility between whomever poses a challenge and whomever it is aimed at/resolves it. Those could both be players. PvP for example is perfectly feasible in accordance with Czege.
I think there are other issues with GM-less games. They can be, and have been, resolved in various ways I guess. I've not really explored this type of play myself, but I'm guessing that what
@aramis erak is saying gives us some pointers. We could potentially distribute parts of the BW GM role amongst players, but then that would kind of imply a certain divergence of their aims would be needed!
@pemerton also addressed the 'supervenient role' of 'big picture' that would need to be addressed as well. My guess is that GM-less games are mostly restricted to less open-ended types of scenarios where the logic of the situation largely drives overall play and pacing. I could imagine a GM-less Cthulhu game, for example. We already know that in the end the PCs are going mad/getting eaten by shoggoths/becoming haunted by Hounds of Tindalos/etc. I think it would be pretty easy to generate scenarios that could be played through without a GM, and most of the game would revolve around A) which of the mythos tropes you encounter and the fun of describing them, and B) which of the above fates actually catches up with any given character.