What's the matter with Lindsey Graham?

So, Lindsey Graham's amendment to the Military Authorization bill passed. This amendment strips federal court jurisdiction to consider habeas corpus petitions from people who have been declared enemy combatants. In practice, this means that if you end up in Guantanamo for no reason whatsoever, you have essentially no way to prove this. So my question is whether or not stripping jurisdiction for writs of habeas corpus constitutes a suspension of the writ for those people, and then whether or not Article I, Section 9, Clause 2, applies to non-citizens in American custody?

[Rest of this post on hold while I decide to read articles on jurisdiction-stripping rather than read for class tomorrow.]