The lawsuit alleged 7 grounds:
Counts 1, 2, and 3 invoked federal jurisdiction under the Alien Tort Statute, 28 U.S.C. § 1350, and alleged violations of international law. Count 4 alleged violations of unspecified provisions of the Geneva Convention. Counts 5 and 6 asserted Bivens claims for violations of the Fifth and Eighth Amendments to the Constitution. See Bivens v. Six Unknown Agents of Fed. Bureau of Narcotics, 403 U.S. 388 (1971). Count 7 alleged a violation of the Religious Freedom Restoration Act (RFRA), 42 U.S.C. §§ 2000bb et seq.
The DC appeals court ruled the detainees could not sue because they were not "people" within the meaning of the Religious Freedom Restoration Act (RFRA).
On a related note regarding the constitutional rights of the undocumented, the court reiterated the standard: Once a person is living in the U.S., whether lawfully or not, he is entitled to the protections of the Constitution:
...aliens receive constitutional protections when they have come within the territory of the United States and developed substantial connections with this country.” Id. (citing Plyler v. Doe, 257 U.S. 202, 212 (1982) (The provisions of the Fourteenth Amendment “are universal in their application, to all persons within the territorial jurisdiction . . . .”) (emphasis added in Verdugo-Urquidez); Kwong Hai Chew v. Colding, 344 U.S. 590, 596 n. 5 (1953)
(“The Bill of Rights is a futile authority for the alien seeking admission for the first time to these shores. But once an alien lawfully enters and resides in this country he becomes invested with the rights guaranteed by the Constitution to all people within our borders.”) (emphasis added in Verdugo-Urquidez)).
Back to Rasul, et. al. At the time the DC Appeals Court issued its opinion, one of their lawyers said:
“It is an awful day for the rule of law and common decency when a court finds that torture is all in a days’ work for the Secretary of Defense and senior generals. It violates the President’s stated policy, our treaty obligations, and universal legal norms.
Update: The Center for Constitutional Rights has issued this statement on today's cert denial.