I'm curious too.
Of the major Supreme Court cases related to detainee detention Rasul v Bush (2004) held that U.S. courts had jurisdiction over Guantanamo detainees; Hamdan v Rumsfeld (2006) held that the Military Commissions were illegal and improper, violating the Geneva convention; the most commonly cited, Boumediene v Bush (2008) is I think the one he's trying to cite, but it held that the Military Commissions Act enacted following Hamdan v Rumsfeld was an illegal suspension of the right of habeas corpus protection guaranteed to Guantanamo detainees and that they were necessarily afforded Constitutional rights tribunals did not afford. All of them categorically affirmed that detainees cannot be tried by military commissions because they do not afford the same rights as U.S. courts.
The Obama DOJ's recent 2009 update of the Military Commissions Act, with its arbitrary channeling of some detainees into real courts, others into military tribunals, and other still into uncharged and untried permanent detention, is likely to be overturned soon enough.
Every Supreme Court ruling on the subject has concluded the opposite of what Gunny claimed, that in fact military tribunals do not apply to those captured in the war on terror because they do not satisfy the Bill of Rights. The precedent for this was set 150 years ago when The U. S. Supreme Court unanimously ruled that military tribunals used to try civilians in any jurisdiction where the civil courts were functioning were unconstitutional, with its decision in Ex Parte Milligan, 71 U.S. 2 (1866) which has been upheld ever since.
I'm guessing that like his belief that the defense budget accounted for 5% of federal spending, he wasn't lying, just grossly misinformed.