Small God of the Dozens
Hmm. For my games I don't think I'd agree that I own the setting. If the players aren't helping to shape, populate, and impact the setting I've probably done something wrong. Other games are more liken that though, and in those instances you're probably closer to the mark.That's reasonable-ish. My thinking, unpacked a little more: The players own the PCs; the GM owns the setting (to include all places and NPCs and history). The PCs own the story; nothing that the GM owns does. Even the PCs' opposition is really part of the PCs' story (note the way the possessives point). I suspect it's probably indicative of my thinking that in my email missives to the players I always describe myself as DMing for them.
I'm really not sure what you're indexing when you use the word 'own' here in reference to the story. The players don't produce any story absent the GM, so the notion that they own it seems ... odd to me. The narrative, if that's what you mean by story, is produced though the oscillating movement of declaration-result between the players and the GM. I would agree with your statement, at least for myself, that I GM 'for the players' but that doesn't lead me to 'they own the story' as it seems to for you.