this is false, FYI. Please reread the constitution. Sometimes it refers to citizens, sometimes it refers to people. The Bill of Rights applies to everyone.
The fundamental civil liberties protections of the Bill of Rights and Constitution apply to all “persons,” not just citizens. For example, every person in the United States has the right to due process and equal protection; to criminal proceedings that afford a right to counsel, a jury trial and freedom from double jeopardy; to freedom from cruel and unusual punishment; to freedom from unreasonable searches and seizures; and to freedom of speech, religion and association.
The Bill of Rights only applies to "people" within the jurisdiction of the American government. The Constitution is not a document that has extraterritorial force of international extent.
Control in the physical military sense is not the same as legislative jurisdiction. See: http://en.wikipedia.org/wiki/Johnson_v._Eisentrager. E.g. the U.S. may have had control of occupied Baghdad, but that doesn't mean Congress had legislative jurisdiction over Baghdad.
Now, the Supreme Court has decided that Congress has de facto legislative jurisdiction over Guantanamo (in an opinion comparing the historical treatment of Scotland, in which English habeas rights did not apply, to Ireland, in which they did): http://en.wikipedia.org/wiki/Boumediene_v._Bush.
Scalia's dissent was the most legally sensible: 'Justice Scalia added that the Court's majority "admits that it cannot determine whether the writ historically extended to aliens held abroad, and it concedes (necessarily) that Guantanamo Bay lies outside the sovereign territory of the United States."[27] Justice Scalia pointed out that Johnson v. Eisentrager (where the Supreme Court decided that U.S. courts had no jurisdiction over German war criminals held in a U.S.-administered German prison in China) "thus held—held beyond any doubt—that the Constitution does not ensure habeas for aliens held by the United States in areas over which our Government is not sovereign.'
But the Court stopped short of saying that foreigners in Guantanamo have the same habeas rights as U.S. citizens on U.S. soil, probably because of the strained nature of their conclusion that they had any habeas rights at all.
Given slavery was not abolished at the time of independence, it seems likely that the writers of the constitution did in fact not intend to apply rights to all humans as broadly as possible.
That's in the Declaration of Independence not the Constitution. The former is high prose. The latter is a legal document. As a legal document, it cannot purport to give rights to people outside of its jurisdiction.
The Constitution does not purport to give rights to anybody. It declares that certain things are rights and prohibits the US government from violating them.
You're confusing the declaration of independence, a fluff document, with the Constitution, a legal document. Fluffy language aside, in the Anglo-American tradition, rights derive from legal documents (or precedents), and the right to habeas corpus or a jury trial derives from the Constitution and is circumscribed the the territorial jurisdiction of the Constitution.
The Constitution details the authorities and powers that the government has. The government does not assume total power when it is dealing with non-citizens or operating overseas. The Supreme Court has ruled clearly on this in the past.