It appears what pushed Justice Kennedy over the edge may have been the Administration's argument that they can do whatever they want in Cuba because they LEASE (and don't own) Guantanamo.
Justice Kennedy decided that, if that were true, we might as well close up the Supreme Court and just allow the President to do whatever he wants:
The necessary implication of the argument is that by surrendering formal sovereignty over any unincorporated territory to a third party, while at the same time entering into a lease that grants total control over the territory back to the United States, it would be possible for the political branches to govern without legal constraint.
Our basic charter cannot be contracted away like this.The Constitution grants Congress and the President the power to acquire, dispose of, and govern territory, not the power to decide when and where its terms apply. Even when the United States acts outside its borders, its powers are not "absolute and unlimited" but are subject "to such restrictions as are expressed in the Constitution." Murphy v. Ramsey, 114 U. S. 15, 44 (1885).
Abstaining from questions involving formal sovereignty and territorial governance is one thing. To hold the political branches have the power to switch the Constitution on or off at will is quite another. The former position reflects..... that certain matters requiring political judgments are best left to the political branches. The latter would permit a striking anomaly in our tripartite system of government, leading to a regime in which Congress and the President,not this Court, say "what the law is." Marbury v. Madison, 1 Cranch 137, 177 (1803).
These concerns have particular bearing upon the Suspension Clause question in the cases now before us, for the writ of habeas corpus is itself an indispensable mechanism for monitoring the separation of powers. The test for determining the scope of this provision must not be subject to manipulation by those whose power it is designed to restrain.