anyway.

This makes JCL go "I'm not saying..."
... that the character has to be fully owned to address a premise, but that your Premise must be fully owned. If another player can change what premise you can address in play, you won't be happy. And when I say that's where all the real design effort will be, I don't mean it's impossible or tricky; I'm just pointing out that forcing other players to change your character is a no-brainer.

This makes VB go "Still not getting it-"
Typically, we're all addressing the same premise anyway.

This makes SLB go "Maybe"
...he means "theme" and not "premise"? (i.e., a player's individual take on the premise) I can see how, in a poorly-designed system, someone could whack your character with a trait that completely breaks your effort to address the premise.