I think, in the oft-cited examples from BW, that roleplaying would be impossible without the resolutions (We found the tower; I found my brother). I think that in any system that boils down to "The GM Decides" where the GM is convinced/persuaded by roleplaying (along the lines of what I understand
@pemerton to mean by "free narration") that the resolution is directly derived from the roleplaying. I think that in any system or instance where the odds of resolution are affected by what has been roleplayed, roleplaying and resolution are intertwined.
I don't think I fully follow what you are saying here in the context of your discussion with
@FrogReaver, but to the extent that I do follow I think I agree.
I don't really understand what FrogReaver's point about dice is. The use of dice is, generally, to establish what is happening in the fiction when that isn't just being settled via consensus or deferral.
Here are some examples of deferral and of consensus that I think are fairly typical in FRPGing:
A player typically doesn't have to dice for their PC to be wearing a brown rather than a green tunic, because the rest of the table defers to the player. The GM typically doesn't have to dice for the tavern to have a man rather than a woman serving the drinks, because the rest of the table defers to the GM; and nor does the player typically have to roll dice to establish that my PC sits down at a table near the door. Typically no one has to dice to establish the players' marching order or watch order for their PCs, because with a bit of back-and-forth between everyone at the table something is established which everyone agrees to and agrees makes sense in the fiction given the relevant traits of the PCs (eg settling on a marching order might require having regard to PC heights; settling on a watch order might require having regard to how long the spell-users need to sleep to rememorise their spells or regain their spell points).
Here are a couple of examples where I think it is fairly typical, in FRPGing, to look to the dice:
The GM narrates an attacking Orc. The player of the archer responds I shoot it with an arrow. I think it's typical in FRPGing to call on dice to help determine what happens next.
The GM narrates a burst of fire from a triggered magical trap. A player responds I take cover behind my shield. I think it's typical in FRPGing to call on dice - in D&D it would often be a saving throw - to help determine what happens next.
The use of dice in resolution doesn't seem, to me, to have any bearing on whether we are
roleplaying or not. Saying
I wear a brown tunic or
I sit down at a table near the door isn't any more roleplaying than
I shoot the Orc with an arrow or
I take cover from the blast behind my shield just because no one will call for the dice to be rolled in order to accept the statement as true in the shared fiction.