The truth was, Team America wasn’t actually called Team America. It was a nickname they chose for themselves, after the movie by the “South Park” creators — a sendup of patriotism that they knowingly repurposed as actual patriotism. Their official name was Team I.D.S., for International Defense Systems — a military supplier that specialized in tactical equipment and ballistics gear. In keeping with the corporate outsourcing of war, I.D.S. was a sponsor of the competition. The team was here not to represent the United States, but to promote the brand.

“Our guys are SEALs, S.R.T.” — special-response teams — “SWAT, ex-Secret Service,” Sebastian Van Duin, a consultant for I.D.S., said. He was a former intelligence specialist from the French Foreign Legion, who knew the team’s leader, Fred, from a job overseas. (What kind of job? They would rather not say.) A former special agent for the Department of Homeland Security, Fred had chased boats in the Caribbean, drug traffickers through Peru, a sniper in post-Katrina New Orleans and gunrunners in Iraq. For the Warrior Competition, he assembled a crew of guys he knew from his time as an S.R.T. commander in Washington, D.C. Most were ex-military: Brian, 35, had served in an elite Coast Guard unit, and Carey, 35, was an antiterrorism sniper in the Marines. Because they still worked in law enforcement, some undercover, they asked to be identified by their first names. One of them, A., did sensitive work for the government and asked to be identified only by a middle initial. Most of the other teams also requested anonymity for their members for security reasons.

These were self-proclaimed “regular guys” who chewed tobacco, talked camo patterns and sometimes educated one another in the ways of the world. (“Dude,” Brandon said one afternoon, “I just saw two Jordanian guys holding hands! They do that?” “Dude!” A. said. “That’s how you know that’s your bro!”) In idle moments, they would cast themselves in the kind of action movies that celebrate the soldiers they want to be: Brandon was Kevin Bacon. Fred was Bruce Willis. Carey, the “funny, fat guy,” was Jason Statham, “plus 40 pounds.” And A. was Matt Damon — the trained killer.

After some speeches by the Jordanian brass, the teams watched a demonstration by Jordan’s renowned counterterrorism unit, the 71st. A dozen commandos in black balaclavas stormed an Airbus A-300, while a dog named Nero apprehended a bad guy in a bite suit. The finale was a big gun battle that lasted five minutes and involved about $10,000 worth of live ammunition; but, for safety reasons, the spectacle unfolded on a shooting range that no one in the stands could see. It sounded very impressive.

Afterward there was a reception with tea and carrot cake, and the soldiers mingled with diplomats and military attachés. Over in a corner, Team America plotted how to smuggle a bottle of whiskey onto the base. “Hey, look,” Eric said, “they’re giving out free Cokes.” He walked over and stuffed a few in his pockets, to use as mixers later.

The Kingdom of Jordan is shaped like a holstered gun, which isn’t a bad metaphor for the country as a whole. A constitutional monarchy with a well-trained military and a relatively secular population, it is — for now — one of the most stable countries in a very volatile neighborhood: Syria to the north, Israel to the west, Saudi Arabia to the south, Iraq to the east. Jordan’s intelligence agency, the G.I.D., is a close partner of the C.I.A. in the Arab world, and over the past five years, the United States has given Jordan more than $3.3 billion in aid and pledged an additional $200 million to help cope with the refugees who have poured over the Syrian border since August.

Kasotc was aid of a kind, too. The base was built by a U.S. construction firm on land donated by the king and paid for by a Defense Department program that provides weapons and infrastructure to friendly foreign governments. In the opening-day speech, Frank Toney, a retired U.S. brigadier general and commander of the Army Special Forces, who now works as Kasotc’s director, said, “We believe that if your partners are strong, then you will be strong.”