If the API headers are copyrighted, wouldn't any program that uses them be a derivative work? In that light, every Java program is infringing. Every program on earth would be infringing something wouldn't it?
Using a library i akin to put a engine into a car. One could argue that the engine would still be a separate piece and thus not "part of the car", but its a tough sell to do in court. The line that separate "a thing" with "other things" is determined by judges, juries (and in some cases, common sense). In 23 years, no one has dared yet to do so.
Using an API however is like putting your own engine into the car, but it happens to use the same input/output of similar car engines. The GPL do not have a dog in that fight, but FSF argues against such stretching of copyright.
No, for a couple reasons:
1. Those programs aren't distributing the material in question. You, the user, will have independently acquired the JRE. This will have most likely been through non-infringing means, given that Sun/Oracle lets you have it for free, and even if it were infringing, you'd be the one at fault, not the program author.
2. Even if that weren't true, there would still be a couple of options to create a non-infringing program. Only programs that are neither non-GPL, nor those from authors who have some other valid commercial license would be infringing. Not "every Java program".