The constitution was never intended to apply outside the boundaries of US territory. The idea that this or that amendment prevents the US military from detaining a goatherd on the other side of the world is a wholly modern (minority) interpretation that's at odds with reality. It would leave the US completely unable to conduct a war.
The constitution appears to have been intended to apply to the US Government, whatever its actions. It even includes a loophole for conducting a war: just actually declare war. These days that's unfashionable, of course.
