As soon as you pushed your branch to remote (which I tend to do for backup reasons especially after working hard on a solution) rebase only means trouble.
Unfortunately I've met far too many who have your "remote" superstition. I remember arguing this exact point in my last gig, when someone was mad at me for force pushing my own remote branch that nobody else was using nor should have been.
Or you mean that a mistake where you accidentally push to someone else's branch?
The default model that public github uses is good for that: everyone works on their own fork of the repo, and makes pull requests to the shared repo. Nobody pushes directly to the shared repo.