The Bill of Rights applies to everyone within the jurisdiction of the American legal system. It does not matter whether they are citizens or foreign nationals because the Bill of Rights makes no such distinctions and court precedence has held as much since at least the 19th century. Greenwald pulls up a court decision where even Antonin Scalia admits as much.
Pointing out the absurdity of such a claim, Greenwald asks:
There are millions of foreign nationals inside the U.S. at all times -- not only illegally but also legally: as tourists, students, workers, Green Card holders, etc. Is there anyone who really believes that the Bill of Rights doesn't apply to them? If a foreign national is arrested and accused by the U.S. Government of committing a crime, does anyone believe they can be sentenced to prison without a jury trial, denied the right to face their accusers, have their property seized without due process, be subjected to cruel and unusual punishment, and be denied access to counsel? Anyone who claims that the Constitution only protects American citizens, but not foreigners, would necessarily have to claim that the U.S. Government could do all of that to foreign nationals. Does anyone believe that? Would it be Constitutionally permissible to own foreigners as slaves on the ground that the protections of the Constitution -- including the Thirteenth Amendment -- apply only to Americans, not foreigners?