True. If software is subject to copyright, then an API should as well.
One thing that you're missing, however, is that copyright protects an expression from being copied, not any form of functionality. Ergo, it is perfectly okay for software not to do "anything unique or non-intuitive," or even work, to be copyrighted.
Further, a person who re-creates an API from scratch and without accessing the original API violates no copyright even if the code is 100% identical. That said, the likelihood of 20 lines of independently designed code being identical is highly remote.
Just, FYI, I am an IP attorney.
hmmm...copyright of an *implementation* of an API is ok, but the API is just the declared interface to the software component. This has been ruled upon in the past, otherwise software like WINE (on Linux) would be in trouble. It *implements* the Windows API so Windows software can run on Linux but has no Windows code. Microsoft makes the API’s public information so people can right application software for it. Anybody can re-implement the API...and I’m a Software Architect that works with open source software and frequently have to deal with legal issues (GPLv2/3, Apache, etc.).