Same for an algorithm.
What you're saying now is this: forget the protocol, which isn't a copyrighted work, let's look at some program that implement the protocol. If you reimplement you will violate the program's copyright. It doesn't work like that because your reimplementation isn't derived from that program. You probably don't even have any direct access to the program's executable, let alone its source. Think of two reporters covering some news event. The news event itself isn't copyrighted, but each article is. Still, because they're both reporting the same event, they will have the same quotes. Still, they're not infringing on each other because their source wasn't the other article but something (the event) which isn't copyrightable. If your source is something that isn't copyrighted, you can copy it even if some copyrighted work copies it as well.
And again, your argument would work to explain why implementing an algorithm is a copyright violation. It isn't, so you can know your argument is wrong.
None of this, however, is relevant to discussions of works that are not copyrighted in the first place, as they do not even satisfy the most basic necessary conditions, like algorithms and protocols, of which REST "APIs" are instances. The case is about stages 2 and 3; they fail at stage 1. Partial, translated, complete, verbatim etc. copies of non-copyrighted works is outside the bounds of copyright law, and have nothing whatsoever to do with this case.
A reimplementation of a protocol will, by definition, have another implementation that has SSO copyright over the API.