That is because the Congress, in the habeus corpus statute, left the jurisdiction in such matters unspecified. In an older hearing, the SC had to fill in that gap, since habeus corpus is a constitutional right. What Congress could do is to fix the problem by specifying which would be the federal district court with jurisdiction in these cases.
If habeas is a "constitutional right" granted to terrorists in GITMO, then why isn't it a "constitutional right" for POW status prisoners in Iraq?
Andy Jackson: First, that is not what the decision said. What the decision said is that you have to hold a hearing to establish that they are illegal combattants.
Justice Scalia: The Court today holds that the habeas statute, 28 U. S. C. §2241, extends to aliens detained by the United States military overseas, outside the sovereign borders of the United States and beyond the territorial jurisdictions of all its courts. This is not only a novel holding; it contra-dicts a half-century-old precedent on which the military undoubtedly relied, Johnson v. Eisentrager, 339 U. S. 763 (1950). The Court’s contention that Eisentrager was somehow negated by Braden v. 30th Judicial Circuit Court of Ky., 410 U. S. 484 (1973)—a decision that dealt with a different issue and did not so much as mention Eisentrager—is implausible in the extreme. This is an irresponsible overturning of settled law in a matter of extreme importance to our forces currently in the field. I would leave it to Congress to change §2241, and dissent