No. Copyright can be used to protect moral rights, since you can't mis-attribute something you can't copy, but that's only done so in the US because there's no federal law defining moral rights. In places where moral rights are in the law, they are not subject to copyright at all. You can even sell or forfeit the copyright, and you'll still have the attribution rights (which are inalienable).
as far as I know, there are no countries that enforce moral rights but not property rights. (...) Which countries' legal systems do you have in mind?
It doesn't matter. My point was that attribution and other moral rights don't rely on accepting copyright. Whether there are legal systems without copyright is irrelevant to this.
According to the idea that we should not respect property rights (and, like you say, only respect attribution / moral rights), this would allow the company to re-license GPL code under an MIT license, then use the newly MIT-licensed code in ways that were unintended according to the original author (i.e. inclusion in non-GPLed code).
What licenses would those be, if there's no copyright? You're still thinking in a matter formatted by the current US law.
Just because in this hypothetical world copyright has been abolished, doesn't mean you necessarily can do what you suggest. As I said earlier, a law could be promulgated that granted the author the right only to prevent others from using code written by him in proprietary binaries - while not granting him/her the right to restrict any other copying.
My only point is that you don't have to accept & respect copyright - the right to prevent others from almost any copying - to defend other rights. They aren't dependent on copyright; that just happens to be, under current US law, the best way to protect them.