First, I'd still question if "creating story as a byproduct" really is storytelling.
Second, "you can still do that" is entirely missing the point... some players have no interest in telling a story, and making the game "story no matter what" lessens their engagement and enjoyment.
Again, I think "storytelling" is something more deliberate and involved than just being the verb-form of the broad "story is any account of events" formed by tacking "telling" on the end of story.
And what about those players whose enjoyment of the game takes significant negative impact when thinking about the characters as fictional elements, let alone when letting "intentional story" concerns into the equation?