Yes, you need a copy of the header files to compile. You don't need to distribute them, to use the API. Any files you do get a copy of can be copyrighted and licensed to you for the purposes of compilation. There doesn't need to be a blanket exclusion on API copyrights for this system to work. As I said elsewhere, people have been placing copyright notices on header files from the earliest days of C, with no ill effects. This is because licensing is generally liberal, or vendors of libraries by necessity have to allow you to #include if they want you to buy their code.
This is not what Google/Android, Inc. was doing. They copied files to create their own product, and distributed them.
Call me cynical if you want, but I'd say one amici, Microsoft, might be looking for ruling to help them avoid future claims like the one they were forced to settle for similar behaviour with JVM.
Worth noting that the settlement of that case didn't bring software development to a grinding halt. It was almost 20 years ago.