The Ninth Circuit Court of Appeals, in Gherebi v Bush 03-55785 (decided Dec 18 2003) considered the rights to habeas for prisoners at Guantanamo. They found that the prisoners there had the right to habeas, and denied the Executive’s claim that Cuba was sovereign over the Bay, as part of the executive's argument that therefore the prisoners had no claim to habeas rights in US courts.
Prisoners at Guantanamo do have habeas rights, but Cuba is the sovereign over Guantanamo Bay.
Habeas
The fifth amendment restrains the government as regards all persons, so the issue of sovereignty is not relevant to the determination of habeas rights. Wherever the Executive Branch has the power under the Constitution to imprison, the Judicial Branch has the power under the Constitution to grant habeas relief.
Sovereignty
The Ninth Circuit argued that eminent domain implies sovereignty, and that the US has the power of eminent domain under the lease, and therefore is sovereign. However, the US does not have the right to eminent domain under the lease. Here is the relevant text from the February 1903 agreement with Cuba:
ARTICLE IIIWhile on the one hand the United states recognizes the continuance of the ultimate sovereignty of the Republic of Cuba over the above described areas of land and water, on the other hand the Republic of Cuba consents that during the period of the occupation by the United states of said areas under the terms of this agreement the United states shall exercise complete jurisdiction and control over and within said areas with the right to acquire (under conditions to be hereafter agreed upon by the two Governments) for the public purposes of the United States any land or other property therein by purchase or by exercise of eminent domain with full compensation to the owners thereof.
Article III does contain the words “eminent domain”. But these words are preceded by the parenthetical statement “under conditions to be hereafter agreed upon”. Here is the purpose of that clause: The United States shall have the right to acquire, in a manner to be agreed upon, any property that is privately held within the leased area. The "manner to be agreed on" is spelled out in the second part of the lease agreement, and is as follows:
Article I (continued)All private lands* and other real property within said areas shall be acquired forthwith by the Republic of Cuba.
The United States of America agrees to furnish to the Republic of Cuba the sums necessary for the purchase of said private lands and properties, and such sums shall be accepted by the Republic of Cuba as advance payments on account of rental due by virtue of said Agreement.
The US advanced the money to purchase the privately held land to avoid any cash-flow problem with the acquisition, with the advances credited to its account. The US did not exercise eminenent domain in its own courts or in Cuban courts. Although the US had “complete jurisdiction and control”, Cuba retained the power to purchase land within the leased area, to transfer to itself the title to the purchased land, and thereby perfect the title of the land that it leased to the US.
This raises the question, if Cuba retains the right of eminent domain, can they simply evict the USA?
Although the United States began using Guantanamo Bay at that point, it took several years to complete the transactions associated with Cuba’s purchases of private property within the leased areas for handover to the United States. The privately owned land involved six ranches at Guantanamo Bay, where the rest of the territory was already in the hands of the state. U.S. payments to Cuba to cover the cost of buying the ranches - El Cuero, El Ocujal, El Cuzco, El Boqueron, Punta de Caracoles, and Mata Abajo - were not completed until 1906.
Not heaven itself upon the past has power, But what has been, has been, and I have had my hour. Dryden