No one in this thread (neither me nor anyone else) has claimed that "the GPL is copyright"--your reasoning here is pure strawman--but that doesn't change the fact that all possible violations of the GPL are also copyright violations. In the eyes of the law, this is purely a coincidence (even though the GPL was carefully written to ensure that this would be the case). Thus, the violation of copyright and the breach of contract are separate matters to be judged separately.
The GPL explicitly allows anything copyright allows. Thus, all violations of the GPL are violations of copyright law. Not because the law says so, but because it's logically impossible for it to be otherwise.
But because they're separate issues in the eyes of the law, you can still be guilty of both. The contract issue isn't going to be dismissed just because it happens to involve copyright violation. Even though all possible contract violations happen to be copyright violations, the law is still going to judge on a case-by-case basis, since the GPL is a contract/license, not a law.
So, the bottom line is that the OP's claim ("violating the GPL is violating the law") is true, not because the GPL is part of copyright law (your bizarre strawman theory), but because only actions which would otherwise violate copyright law are capable of violating the GPL. There doesn't have to be an explicit legal link if one set of actions is a strict subset of the other. Which it is.