Sovereignty and the Court

Today the LA Times has a story on a recent court ruling that

In a victory for the White House, a U.S. appeals court Tuesday threw out the legal claims brought on behalf of the hundreds of prisoners held at Guantanamo Bay and ruled that they did not have a right to plead their innocence in an American court.

threw out legal claims of prisoners held at Guantanamo Bay. The story notes:

In a 2-1 decision, the judges said the Constitution did not extend the right of habeas corpus to noncitizens held outside the sovereign territory of this country. “Cuba — not the United States — has sovereignty over Guantanamo Bay,” Judge A. Raymond Randolph wrote.

Let us say this goes to the Supreme Court, and the Supreme Court rules the same way based on the same reasoning. (I understand its not an unreasonable assumption.) Here are is a question for our readers who are attorneys or otherwise have a good understanding of the law:

What happens when Cuba decides to exercise this sovereignty given to them by the US Courts? I understand Guantanamo has been a thorn in the Cuban side since Castro overthrew Batista. (i.e., since one SOB overthrew another SOB)

As a follow-up, if Scalia and Thomas and Alito and Roberts and one more of the, um, towering legal minds on the Court decide that Cuban sovereignty only applies when it benefits the administration, and not when the Cubans decide to exercise it, what happens to the American concept of property rights?