Explicitly. You can't share branches between repos, but git does a good job of making it look like you can. master and origin/master in your repo are physically different things from master in someone elses.
I don't mean to single you out but I've seen developers with really, really nutty workflows because they didn't understand this.
The implicit branch here is any local code. It's clearly diverging from the authoritative repo (whatever that is for your workflow and VCS)
My point was that any workflow that doesn't operate in a shared source directory already has those local "branches". You might as well acknowledge it and roll with it.
(Doesn't diminish your point about master & origin/master. I think this link is a propos to that: http://wheningit.tumblr.com/post/32959730634/when-the-office... )
Two branches are two branches, even if they point to the same commit. Update one branch, the other remains unchanged.