Bedrockgames
I post in the voice of Christopher Walken
I think any definition of RPG which doesn't include the idea of creating some sort of narrative through play misses the mark pretty well. By the same token, I certainly do think you can play an RPG without roleplaying, the same way you can play a board game with roleplaying.
This is a matter of viewpoint and how one defines "story". I am pretty comfortable talking about story to mean "in game events" but it is a slippery term and can mean more than that. So you do get a lot of folks who reject the idea of story being in an RPG (basically because there are folks who make the leap from "story is present in an RPG" to "RPGs must serve story more than anything else"). Does story emerge naturally through the actions of the players? Sure, I have no problem with that. But does that mean that I am there to be entertained by a good yarn rather than to play a character in a believable world that feels real and doesn't follow the rules of a good story? Personally I don't like it when GMs start doing things "for the story", I am much more of a let the dice fall where they may, let stuff happen without concern for drama or pacing, kind of player. So I think some of the resistance you see to "RPGs are collaborative storytelling" comes from the fact that that often gets used to either say RPG mechanics should work to create a good story or that the ideal session produces a good story. But lots of people are not interested in that kind of game. In short, I think RPGs are collaborative storytelling is a fine definition provided the next sentence isn't "therefore good RPGs should have narrative mechanics" or something.