There's lots of previous caselaw in the U.S. suggesting API's are not copyrightable, basically on the theory that functionality itself, as well as factual statements or descriptions of something, are not copyrightable.
For instance, if you write a recipe, the -exact text- of that recipe is copyrightable, but the actual recipe itself is not -- someone else can reword it in their own words, with the same basic ingredients combined using the same operations, and that is not protected by the recipe-writer's copyright. This is (or was?) established in U.S. law.
Similarly, in the U.S. _functionality_, behaviors or operations themselves, are not copyrightable (although it may be patent-able). You can copy a competitors functionality exactly, as long as you do it with your own original implementation -- the functionality is not protected by copyright. (This is why people do 'clean room' compatible implementations by developers who never saw the original code they are copying the functionality of). In general, the right reverse engineer and reproduce the functionality of a technical work without the permission of the copyright holder of the original work -- is (or has been?) legal and protected.
(I am not sure the judges involved realized the relationship between promoting the copyrightability of API, and what this does to the previously well-established right to reverse engineer and create compatible things).
So the belief, previous to this case, was that an API is more like functionality, or the steps in the recipe. An implementation of an API is copyrightable -- but the description of the API itself, the classes, methods and signatures, are more like functionality or statements of fact, more like the steps of a recipe or a description of behavior. Both of which are not copyrightable -- you can't prevent someone from "doing the same thing", only from copying your particular code or text), then they are like a creative work in fixed medium themselves (the exact text of a particular written recipe, or a particular code implementation. (Patent law lets you prevent others from 'doing the same thing', but that's a different law with different requirements for what is patentable vs what is copyrightable, different legal rules for determining if a violation occured and what the penalties are, etc.)
You are (or were?) allowed to copy an API in your own implementation by reverse engineering in order to create a compatible implementation, and it doesn't make a lot of sense if you lose this right because you can get the API from docs instead of reverse engineering it.
I'd imagine you can get more details from various briefs involved these cases, as far as cites to specific previous law. But to many, the fact that API's are not copyrightable is what's consistent with existing law over copyright, including the lack of copyright over the actual operations of a recipe themselves and the protected ability to reverse engineer someone elses thing to create your own compatible implementation. It seems to many that making API's copyrightable is inconsistent with much existing law.