You are correct. (For the unfamiliar, there are separate rulings because in this case, the Court of Appeals for the Federal Circuit ruled that APIs are copyrightable, then remanded back to the district court to re-try the case in light of the new decision about copyrightability, which then found that reimplementation of the API was covered under fair use.)
Only in the US. In the EU, in particular, APIs cannot be copyrighted[0].
Namely: "For the avoidance of doubt, it has to be made clear that only the expression of a computer program is protected and that ideas and principles which underlie any element of a program, including those which underlie its interfaces, are not protected by copyright under this Directive."
