Actually, the prisoners status usually defines what rights they get or not, not where they are from, per the conventions and law of landwarfare...not the consitution. The constitution treats such treaties as binding and part of US law, thus we get stuck with having to use something that wasnt really very well written in consideration of terrorists and insurgents.
I mean, if you want to confer POW rights or status to these folks then the absolutely correct venue to try them would be a courts martial as that is what international treaty dictates should be done.