You quoted the "media" instead of the actual statement.
Which doesn't contain what your source claims.
The statement: http://www.whitehouse.gov/news/releases/2005/12/20051230-8.html
And people say the liberal media is losing influence...
The executive branch shall construe Title X in Division A of the Act, relating to detainees, in a manner consistent with the constitutional authority of the President to supervise the unitary executive branch and as Commander in Chief and consistent with the constitutional limitations on the judicial power, which will assist in achieving the shared objective of the Congress and the President, evidenced in Title X, of protecting the American people from further terrorist attacks. Further, in light of the principles enunciated by the Supreme Court of the United States in 2001 in Alexander v. Sandoval, and noting that the text and structure of Title X do not create a private right of action to enforce Title X, the executive branch shall construe Title X not to create a private right of action. Finally, given the decision of the Congress reflected in subsections 1005(e) and 1005(h) that the amendments made to section 2241 of title 28, United States Code, shall apply to past, present, and future actions, including applications for writs of habeas corpus, described in that section, and noting that section 1005 does not confer any constitutional right upon an alien detained abroad as an enemy combatant, the executive branch shall construe section 1005 to preclude the Federal courts from exercising subject matter jurisdiction over any existing or future action, including applications for writs of habeas corpus, described in section 1005.
That's the section in question. .
Thank you for that URL. It defined things very clearly.