That’s incorrect. From wikipedia:

“An agreed condition between Cuba and the United States to secure the withdrawal of United States troops from the island was Cuba’s adoption of the Platt Amendment. The amendment was a rider appended to the Army Appropriations Act, a United States federal law passed in March 1901 which was presented to the U.S. Senate by Connecticut Republican Senator Orville H. Platt. The Platt amendment stipulated that the United States could exercise the right to intervene in Cuban political, economic and military affairs if necessary, and replaced the less specific Teller Amendment. It was to define the terms of Cuban-U.S. relations for the following 33 years and was bitterly resented by the majority of Cubans. Another consequence of the amendment gave the United States continued use of the southern portion of Guantánamo Bay, where a United States Naval Station had been established in 1898. The lease of the bay was confirmed by the Cuban-American treaty which was signed by the presidents of both nations in February 1903.”

Several years back I remember Haitian refugees were being housed in Guantanamo. Some children were born there and the parents were trying to claim American citizenship for them. The US basically told them, “Sorry, but we don’t own Guantanamo, we just rent it. They’re Cubans.”