I don't think it's the rerunning that's the problem, but the misattribution, claiming others' work as their own or denying them credit (and presumably royalties).
Compare e.g. someone being jailed for resisting arrest when there was no justification for arresting him in the first place.
The law doesn't care whether you claim a copyrighted work is yours or not. It cares whether, if you copy a copyrighted work, you have the license to do so.