Well, if there's reason to believe they're up to no good, then yes, they should be imprisoned and interrogated. The nations of which these people are citizens may certainly interpret it as an illegal act, and may take things up with our government if they wish.

I'm not going to lie to you and say I'm 100% okay with Gitmo and what it stands for, or that imprisoning even non-citizens indefinitely is a sane way to run things. It just needs to be made clear that the US Constitution is a covenant for US citizens, so those who try to apply it to everyone in the world don't have a leg to stand on.