Is habeas corpus for non-citizens?

Today, President Obama signed four Executive Orders, some of his first substantive exercises of his new executive powers. One of those orders addressed the longevity of the prison camp at Guantanamo Bay, Cuba, which our military has used for years to hold so-called "enemy combatants."

One of the findings of this particular Executive Order reads as such:

"The individuals currently detained at Guantánamo have the constitutional privilege of the writ of habeas corpus. Most of those individuals have filed petitions for a writ of habeas corpus in Federal court challenging the lawfulness of their detention."

I know the Constitution explicitely denies the removal of such a protection in Article I, Section 9:

"The Privilege of the Writ of Habeas Corpus shall not be suspended, unless when in Cases of Rebellion or Invasion the public Safety may require it."

What I am unclear of is the history of this protection and whether it is extended to non-citizens of this country. I tried doing a little research, but found myself rather tied up in knots trying to follow the breadcrumbs of this topic through 200 years of case law. Being that blogging is not my full-time job, and law is only an armchair interest (at least until I send myself to law school), I don't have the time or patience to unravel this mystery.

Perhaps my sister, a first-year law student, or one of my several other legally-inclined family members can help me navigate this and understand (a) What was the intent of the Framers when it came to the rights of H.C. and non-citizens? (b) What is the most recent constitutional understanding of H.C. in this regard? and (c) How recently has it changed, if at all?

Was Obama accurate in his finding that habeas corpus does extend to non-citizens?

I'm not arguing one way or the other the moral aspect of any of this, simply the constitutionality of it.