By 6 to 3, the court ruled that the president went too far in 2005, when he decreed that the states had to abide by a 2004 decision by the World Court. That decision found that several dozen Mexican citizens who had been sentenced to death in the United States had not been given the assistance from Mexican diplomats that they were entitled to receive under an international treaty....Here's Roberts's opinion.
Mr. Medellin’s conviction and sentence were upheld in the Texas courts despite the 2004 finding by the World Court, and the Supreme Court concluded on Tuesday that President Bush had no authority to order the state courts to reverse themselves, no matter what the World Court said....
The Supreme Court ruling acknowledged that President Bush, in pressing Texas to take another look at the Medellin case, was acting on behalf of the “plainly compelling interests” of fostering observance of the Vienna Convention and trying to maintain good relations with other countries.
However, the ruling added, “The president’s authority to act, as with the exercise of any governmental power, ‘must stem either from an act of Congress or from the Constitution itself.’ ” The language cited was from a 1952 ruling in which the high court found that President Harry S. Truman did not have the authority to have the federal government seize and run steel mills.
UPDATE: Here's the Wall Street Journal article, which emphasizes the insulation of the state courts from the dictates of the international court — on treaties that the U.S. has signed:
Treaty obligations, in other words, do not necessarily take on the force of law domestically. Rather, Congress must enact legislation for whatever provisions -- such as consular notification -- that it wants to make the formal law of the land. This distinction matters because it establishes a fire wall between international and domestic law. It also protects the core American Constitutional principles of federalism and the separation of powers. As Justice Roberts points out, the courts must leave to the political branches "the primary role in deciding when and how international agreements will be enforced."Of course, President Bush attempted to take the action necessary to make the treaty obligation enforceable in state courts, and this is the exercise of power that the Court rejected.