Not exactly; an API can be completely re-implemented from scratch and still be compatible. If it was just about the API code, there wouldn't even be a case.
The idea that an API could legally be an "original work of authorship" makes a lot of sense; but the technical implications could indeed harm the industry overall.
Essentially what this means is: I build a system, you're not allowed to build a compatible system. Yet another reason why open source is the only way forward.