That's the way traditional gaming is played out.
You go to a convention, and you pay money for a GM to weave a story for you. It's almost like paying to gpo and see a movie, axcept that you can manipulate the story toward one of a few defined conclusions that the GM has prepared.
You play around a table with friends, one takes on the responsibility of setting up the stories, while everyone else creates caharacters to take part in those stories. Sometimes the group has an adversarial relationship with their GM, working to subvert the stories; other times it's cooperative.
But games need not always be like this.
I've alluded to cooperative storytelling in quite a few of my posts, but checking back through the weekly game mechani(sm)s I don't think I've actually brought up the notion as a specific topic. It's something that has really helped to define the new generation of roleplaying games (particularly those designated as "Story Games" and many games belonging to the Forge diaspora).
Sharing the narrative responsibilities isn't a comfortable idea for a lot of people who are happy to "sit back and be entertained". Yet, the other extreme is often considered just as unpalatable, a phenomenon known as "railroading".
But I've always run games ina collaborative manner, bouncing ideas of the actions of the characters rather than instituting specific storylines...and I've been told that my games as far better than those of a lot of other GMs. The step that causes most traditional players a levcel of trepidation is the idea that they can help shape the world around their characters, not just the actions of their characters in response to that world.
In Guerilla Television, I forced this step apon players by having a player begin a scene with a player on one side adding a sentence of description to the setting, while the player on the other side had a chance of introducing a complication into the scene. As GM, I just facilitated the events unfolding and reined in certain players when their descriptions started getting too long winded, or just didn't fit the events of previous scenes.
I also used a metagame currency to allow players to introduce scene framing elements in The Eighth Sea. The games run at Gencon last year gradually refined the notions and once the game was actually played according tothe rules I'd written, they worked well.
Yet, both of these games have definitely revcealed the fact that not all players enjoy the shared narrative reponsibilities.