> The problem with foreigners having rights is that it goes against very deep principles in the western tradition.

Except the Supreme Court has upheld various rights foreigners have w/r/t the bill of rights.

When I say "foreigners" I mean people who are neither U.S. citizens nor on U.S. soil. See: http://www.salon.com/2010/02/01/collins_5.

See in particular his quote from Scalia's dissent in Boumediene:

“The alien, to whom the United States has been traditionally hospitable, has been accorded a generous and ascending scale of rights as he increases his identity with our society . . . .

“But, in extending constitutional protections beyond the citizenry, the Court has been at pains to point out that it was the alien’s presence within its territorial jurisdiction that gave the Judiciary power to act.” Id., at 770–771.

Not even Glen Greenwald claims that the U.S. Constitution applies to non-citizens trying to board a plane in Cairo.

What subset of the federal government is considered the sovereign entity here?

I don't really understand this. Judges are part of the government, so how is allowing judges to actually judge things at the border a violation of sovereignty?

I'm talking about rights, not laws. Congress could, for example, pass a law requiring immigration officials to give certain process to people denied visas. Judges could enforce those laws, and nothing about such a scheme would violate sovereignty.[1] But saying that foreigners have a right to such process is different. Where does this right come from? Foreigners are not parties to the Constitution so it can't come from that. It has to come from something "bigger," some higher law that encompasses both the foreigner and the U.S. But unless you believe in some sort of God and divine law, there is no such thing. The sovereign entity is the end of the line--nothing binds its actions other than its own conscience.

[1] Though many people would say it's a separation of powers violation.