> I don't think can't just go about relicensing a project willy-nilly, even if it is BSD

The whole distinction between permissive and copyleft license is that the former allows downstream relicensing on substantially different terms with very little restriction (typically, something like requiring retaining the original copyright and disclaimers.)

It probably legally requires enough new creative work for the downstream version to be an original derivative work and not a mere copy that wouldn't be eligible for a distinct copyright, but that's still a lot less than a copyleft -> permissive replacement, which requires reimplementation rather than derivation.