Can We Arrest These People?

Got into an argument last night about Constitutional protections for terrorist suspects. With a lawyer. She seemed to think Constitutional protections should apply to suspects - even if they are non-citizens. The example she gave was that legal and illegal aliens in the US are protected by US laws. Okay...

So if that's true, then should non-US citizens in foreign countries also be subject to prosecution if they break US laws? Like, in this case, threatening to assassinate President Bush publically?

Well, she would say, no, of course. But I'm not sure how the logic stands up. Actually, yes I do.