The disconnect is in part because of Guantánamo’s long history. It is the oldest United States military installation on foreign soil, leased from Cuba since 1903 after the Spanish-American War, when the U.S. Navy realized that the deep water harbor halfway between Atlantic ports and the Panama Canal would be an ideal point for ships to take on coal. For decades it was also the winter training hub of the Atlantic fleet.In recent times, the 45-square-mile Navy station, with its clear waters and murky legal status, has also served as a kind of constitutional Room of Requirement where the federal government could park people it needed to be close to the U.S., but, for legal reasons, not actually in it.

In the 1990s, more than 50,000 Cuban, Haitian and Chinese refugees were held in tent cities at the base — a temporary haven outside the jurisdiction of American courts. The same attribute made it attractive to hold enemy combatants in the so-called war on terror after 2001.

On my visit, the split between American and un-American popped up in unexpected ways. The base is home to a menagerie of endangered animals, including a flourishing population of Cuban rock iguanas. The cat-size lizards are protected by U.S. law, even though human detainees here are not.

Many in legal circles have worried that the current setup at Guantánamo could amount to a legal version of Jurassic Park, where precedents in holding people without charge could somehow escape the island and begin preying on mainland legal protections. And for all the small-town America feel here, occasional reminders show up that you’re not in Kansas anymore. Red stickers on the desk phones provided for reporters note that all conversations are subject to monitoring.

But most people living at the base seem to pay the secret side of Guantánamo little mind. The majority of residents have nothing to do with the prisons, and know little about what goes on within. And the troops who are familiar with both sides of Guantánamo can toggle back and forth in a way that would feel absurd anywhere else. One morning, an Army sergeant assigned to be my minder went through the photos on my camera one minute, deleting photos the military chose to censor, then put the camera down and offered me advice on a few good places to go snorkeling.