I can understand a Copyright license for source code that is published (e.g. the GPL) because its easy to see exactly what's being protected against copying, not to mention it protects against against a very specific threat -- using the source code to compile your own unauthorized software. On the other hand, companies that don't open their source code should theoretically only be able to enforce copyright laws against someone who's accessed & stolen source code and used it to compile unauthorized software. I don't understand how it can be used to combat piracy when then source code was never involved in the act.

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Copyright protects the creative work -- whether it is artwork, maps, stories, poems, software, whatever -- from being copied, published or distributed without their permission. It doesn't matter if the company has made the work public or not -- the work cannot be copied or distributed without their permission. But your example makes a false assumption -- the company has copyright over BOTH the source code AND the compiled executable or object code. So, they can press claims for unauthorized copying of the executable without a license, regardless of whether the source code is copied.