The Constitution is quite clear on the matter. It outlines what the U.S. government is permitted to do. Anything not permitted in the Constitution is forbidden to the government. There is no clause that says outside of the U.S. anything goes.
Any weak excuses to the contrary are further damaged when the action is taken against a U.S. citizen.
And as a final death blow, are they trying to claim that if a wanted criminal was spotted in the international concourse of an airport, they would just watch as he boards a plane bound for Argentina because there was no jurisdiction there to arrest him? Or would the U.S. government suddenly assert territorial rights?