Collaborative tends to imply not unilateral. I'm describing something that is unilateral, and hence is not collaborative.To at least some extent, you're having a sematic argument. To some people allowing a player to do some of that is collaborative authorship. You don't have to agree with that, but its absolutely how they see that.
Like in AD&D I get to decide what race my PC is (subject to ability score requirements). That's not collaborative authorship of the fiction, and I've never heard it described that way. It's just me deciding.