The government, in response to the plaintiff's brief in Boumediene v. Bush, which claimed a "common law constitutional right" to habeas corpus, has issued a supplemental brief to contradict the argument for this particular interpretation.
From Ben at SCOTUSblog:
The Court has said that the scope of habeas rights at the current time depends in part upon their meaning in past history, especially in 1789. At that time, [U.S. Solicitor General Paul D.] Clement argued in the new brief, there was a common-law rule that a confined individual seeking release “was not permitted to controvert the facts” the government had cited for the confinement. That rule, along with geographic limits that the government argues restrict habeas rights, would have kept today’s detainees from “obtaining anything like the review” they will receive if they challenge their detention in the D.C. Circuit Court under the Detainee Treatment Act.Ben left out the third reason Clement cited for the detainees lack of access to habeas. The brief says, "That common law rule, together with the geographic limits on the writ and the historical unavailability of habeas to 'prisoners of war,' would have precluded petitioners from obtaining anything like the review they receive under the Detainee Treatment
Act of 2005."
This historical unavailability assertion was supported by saying:
Post-1789 British cases underscore that the British courts did not view prisoners of war as a specialized class, but used the phrase generically to refer to enemy combatants. Indeed, the “prisoner of war” label was even extended to a non-combatant German national who had been resident in England for 25 years. See, e.g., The King v. Superintendent of Vine St. Police Station, 1 K.B. 268, 278 (1916) (Eng.) (If the executive “represents to this Court that it has become necessary to restrain the liberty of an alien enemy within the kingdom, and treat him as a prisoner of war, he must be regarded for the purposes of a writ of habeas corpus as a prisoner of war.”).