The Copyright Act, however, is; if APIs are protected by copyright, than making a derivative work of an API is an exclusive right of the copyright owner.
Which is a key reason why there is widespread concern about the CAFCs ruling on API copyright. (OTOH, Google losing on fair use at the CAFC makes it more likely that the API copyright issue gets to the Supreme Court in this case rather than a later one, so it might be a good thing for resolving that concern.)
No literal copying of text is required for something to be a derivative work. Transforming a work implementing an API into documentation describing the API would produce a derivative work of that API, if the API is protected by copyright. Transforming that documentation of the API into another implementation of that API would also produce another derived work of the API.
Coypright covers derivative works of copyright-protected works, as well as literal copies. If APIs are copyrightable, there is a very good case to be made that a reimplementation of an API implementation (not an API that serves a similar function, but an actual reimplementation) is a derivative work of the API itself.