Doesn't the Linux kernel group hold a very similar stance in that you cannot use the kernels internal APIs without breaching copyright and thus falling under the GPL as a derivative work?
Using the API doesn't invoke the GPL -- it's actually the linking process. When you link against the kernel, your binary becomes a derivative work partially based on the kernel. Since the kernel is covered by the GPL, creating any derivative work from it requires you abide by the terms of the GPL. I doubt any FSF lawyer would have anything negative to say about cloning a project's public API in order to create a completely new implementation under a different license.
Another example: If I created a GPL program with an API that did not make it necessary to link against a library to use - e.g. you talked to my program via IPC or a wire protocol like SOAP, then you could utilize my API all you wanted without triggering the GPL. You could distribute your program that uses my API under whatever license you want.
This is why it's common for software that has a GPL server component to distribute the client driver libraries under the LGPL. Modifications the the server or the client driver itself must be shared, but programs that merely link to the driver may remain proprietary.