Yes, it's true that the Constitution only applies to American citizens. There is, however, another important document outlining the culture of liberty that the US stands for (or at least used to stand for). It clearly states:
All men are created equal.
Not just all men born in the USA. All men.
Further, we did, as Big Rob pointed out, sign agreements to treat POWs with human decency. Therefore, we dare not call the detainees of this war prisoners of war, because that would require us to treat them with human decency.
Saxon observes this:
Which, of course, automatically assumes that anyone held by the US military as a terrorist is guilty of terrorism. We know, of course, that is not the case.
If all men are created equal, if we would neither torture our own citizens nor our prisoners of war, if we believe in the principle that a person is innocent until proven guilty, how can we possibly justify inventing a new term to describe people in our custody, then treating them in a manner that would be illegal were they either citizens or POW?