I could be wrong, but I thought the GPL basically said "anyone who has access to the binary must have access to the source code". This is why you're allowed to write a webserver with GPL libraries without having to worry about releasing the code to the users (unless it's AGPL), since the users don't have access to the binary, just the stuff that the binary is producing.

If that were the case, I think they'd be in the clear legally to use Linux as long as they offered to provide the source code to anyone in the military who had access to the binary, which wouldn't be the general public.

That said, just to avoid the headache, I'd probably choose FreeBSD as well if I were in charge of the Chinese military.