I have no idea who was spied on, but the Executive Order doesn't seem to make any such distinctions. Moreover, if they took the time to verify immigration status, why couldn't the Administration's people have gone to the FISA court to get a proper warrant? The FISA court almost never turns down national security requests and it is extremely speedy to boot.
Do you, or anyone else know anything about the FISA court? How many members does it have? How is someone nominated to it? What's the confirmation process? What's the current makeup? How many Clinton appointees? Has Bush appointed anyone?