And what is copied verbatim are just the headers
If you are using different languages that compile to a compatible target, or if you are using the same language that admits different literal declarations expressions that produce the same interface, it is possible to have an API reimplementation -- for the same target platform even -- that does not involve verbatim copying of even the headers/declarations.
For example, in C, this would involve function name aliasing which is usually a compiler specific extension. This might give you name compatibility, but to get struct-level compatibility, you'd have to copy the exact layouts due to padding issues.
In C++ it's even harder, due to when vtables are emitted, etc.
My java knowledge is old (java 5), so i don't know if they made it possible.
Objective-C, I believe it would only be possible if you used the runtime reflection methods directly. I don't think you can easily do it with just headers (corrections welcome!) etc
Though both making verbatim copies and making derived works are exclusive rights of copyright owners so that doesn't really reduce the impact of API copyrightability on API reimplementations,