In response to my most recent item on Guantánamo Edward Hasbrouck asks this reasonable question: “if courts in the USA say Guantanamo isn't under their jurisdiction, doesn't that mean they would have to recognize Cuban jurisdiction?”
The answer to this question is unusually clear: No.
The US has signed two treaties with Cuba that relate to Guantánamo. In 1903 the US and Cuba signed a treaty (US Treaty Series No. 426) which provides,
While 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.
The more recent treaty, the Treaty Between the United States of America and Cuba of 1934 (US Treaty Series No. 866) abrogates the 1903 agreement in Article I, but then in Article III states,
Until the two contracting parties agree to the modifications or abrogation of the stipulations of the agreement in regard to the lease to the United States of America of lands in Cuba for coaling and naval stations signed by the President of the Republic of Cuba on February 16, 1903, and by the President of the United States of America on the 23rd day of the same month and year, the stipulations of that agreement with regard to the naval stations of Guantanamo shall continue in effect. The supplementary agreement in regard to naval or coaling stations signed between the two Governments on July 2, 1903, also shall continue in effect in the same form and on the same conditions with respect to the naval station at Guantanamo. So long as the United States of America shall not abandon the said naval station of Guantanamo or the two Governments shall not agree to a modification of its present limits, the station shall continue to have territorial area that it now has, with the limits that it has on the date of the signature of the preset Treaty.
So the Gitmo provisions survive until the US and Cuba agree to change them. And Cuban courts have no jurisdiction to intervene.
Personally, I would be prepared to read the words “the United States shall exercise complete jurisdiction and control” language of the treaty as invoking the powers of all three branches of government, not just the executive. In this view, under Art. VI of the Constitution (“This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any state to the Contrary notwithstanding.”), the treaty would supply the jurisdiction for the federal courts that they seem to believe they lack under Article III.