(Courtesy Liel Leibovitz)

As you step off the plane, cross the tarmac, and amble into the terminal at V.C. Bird International Airport in Antigua, the first thing you see is a 7-foot-long blue marlin, made of plastic, mounted on the wall, a small plaque beneath it claiming that the original, weighing 771 pounds, was the largest of its kind ever caught in the West Indies.

It’s a fantastic monument, not only because the fish—its expression resembling that of a teenager rudely awoken from an afternoon nap—looks thoroughly fake, but also because it suggests to the uninitiated traveler that beyond the terminal’s gates lies a world of wonders, strange creatures and all.

In a sense, this is precisely the feeling the Antiguan government is interested in promoting. More than 300,000 tourists, on average, descend on the island’s shores each year, a horde of salmon-hued Brits and beer-battered Germans that both sustains and overwhelms the local population, estimated at 72,000. There’s little the Antiguans can do: Tourism accounts for more than 60 percent of the island’s economy, leaving the locals with no choice but to vigorously market their tiny nation as a magical Caribbean getaway, a sort of real-life Fantasy Island. Along these lines, the fish is a monument to the impossible: St. Bart’s may have the reputation, and Mustique the celebrity appeal, but only in Antigua, the marlin suggests, may the very laws of nature be bent for your amusement.

Last week, my wife Lisa and I flew to Antigua for a weekend to attend the wedding of Mr. B., a hotelier, at his lovely Antiguan resort. Much time was spent pondering what to wear—the groom threatened to beat up and toss out any guest who dared wear a tie—and very little contemplating such minor issues as entry visas. If Israeli citizens needed a visa to visit Antigua, I told myself, Mr. B.’s son-in-law, himself Israeli and my close friend, would surely have let me known.

But no sooner had we landed and admired the oversized fish than an immigration official broke the doleful news: no visa, no entry. Meekly, I removed my baseball cap and shades and said that I had no idea I needed a visa, an idiotic statement that seemed to elicit more pity than disgust. “Well,” said the immigration official, “you do.”

There was no other choice. I invoked Mr. B.’s name. This had the desired effect: Lisa and I were removed from the line, taken to a secluded spot by the nurse’s office, and instructed to wait. Soon, another official, smiling warmly, moseyed over and told us that she’d do whatever she could to help us resolve our little problem as quickly as possible.

Veteran travelers, we refused to succumb to panic. Instead, we pulled out our phones and texted Mr. B.’s daughter, informing her of the snafu. Two minutes later, there she was, beaming, standing by our sides. There was no point in asking how she’d gotten through security, immigration, and all the other barriers that are supposed to stop you from walking right into an airport’s secure detention spot. A few words were exchanged, and it was agreed that I would be released on my own recognizance, passport unstamped, and sent to the Ministry of National Security to settle my affairs.

The Ministry of National Security is located in downtown St. John’s, across the street from a Subway sandwich shop, in a building that looks more suited to botched drug deals than to any official matter of state. The posters on the wall make clear the ministry’s main concern; most of them warn against abduction and modern-day slavery and feature a host of pink figures engaged in subservient activities, from forced intercourse to mopping floors. The ministry’s employees, however, were unperturbed: R&B ballads roared from the tinny speakers of a far-off computer, and most officials, dressed in blue-and-white uniforms, seemed as unburdened as only those entrusted with defending a thoroughly unthreatened Caribbean nation can be.

Accompanied by our friends and Larry, Mr. B.’s lawyer, we located the right official and pleaded our case. The official, a woman in her fifties, was baffled. You were already allowed into the country, she said as she looked at my unstamped passport, you may as well just stay.

Larry, a former LAPD police officer and a man with many connections on the island, asked for a moment alone with the official. A few minutes later, he came out and said quietly that he thought he figured out the entire mess. Antigua, he said, had a diplomatic relationship with Libya. After Israel assassinated a Hamas official in Dubai last month, the Libyans demanded that Israelis no longer be allowed to enter Antigua, or, at the very least, that they be required to pay a hefty fee for a special tourist visa. The Ministry of National Security, he added, was cool with letting me stay, but it was the prime minister’s call, and we needed to report to the prime minister’s office to sort everything out. Unfazed, we said our goodbyes to the lovely folks at National Security, who saw us off by making us promise to convey heartfelt congratulations to Mr. B. on his upcoming nuptials.

On our way to see the prime minister, however, my mind began racing. Here I was, I thought, in paradise, detained for a crime I didn’t commit. All I wanted was a quick vacation, and instead I was forced to account for my country’s follies. I had left Israel behind, emigrated to America, got my Green Card, opted to abandon the perpetual association with the sort of militaristic shenanigans that lose friends and alienate people. Clichés started swirling in my head: Just when I thought I was out, they pull me back in. You can run, but you can’t hide. You may be through with the past, but the past isn’t through with you.

The car stopped. We were parked in front of a one-story office in the midst of a patch of grass, guarded by a single soldier in a green t-shirt and no gun. In front were two enormous stone lions, the sort popular both in China and in chintzy souvenir shops on Manhattan’s 59th Street. It looked, I whispered to Lisa, like a dentist’s office in a Long Island strip mall.

It smelled like one, too, with the unmistakable odor of acrylic monomer, ammonia, and quiet desperation. Magazines were strewn everywhere, mainly an oversized glossy called China Today. It was a thick hint: Chinese government contractors are in charge of most major construction projects in Antigua, as they are in so many developing countries across the globe. Hence the stone lions. A poster on a nearby wall read: “What will come to us will come to us, so quit your worrying!” I took the advice to heart.

A hospitable secretary greeted us, indicating that the Ministry of National Security had already filled her in on the details. We were asked to pay $40 and received a printed receipt. We were officially welcomed to Antigua and allowed to drive on to the resort.

There, in the shadow of palm trees and in the company of some of the island’s most influential men, scotch and talk both flowed. The Mossad, one tough old developer said with a smile, nearly assassinated our vacation plans. Another advised me to try and avoid killing anyone while on the beach. I grinned politely but stared at the umbrella floating in my cocktail; if everyone already saw me as a murderer, I brooded, I might as well enjoy it.

Gradually, however, my ire subsided, drowned in drink and merriment. The weekend was glorious. When I saw the prime minister himself at the wedding, I smiled politely and shook hands. Antigua, after all, let me in. There was no need for a diplomatic incident.

Tanned and thrilled, we flew back home to New York, where two feet of snow were still piled on the ground. The next morning, we talked about our time as personae non grata in paradise. At a distance, the entire story seemed fantastic. Would Antigua really care about the Mossad? Would a mere visa requirement constitute punishment of Israel and its policies? And would any nation, even one as relaxed about its official undertakings as Antigua, really change its rules overnight and fail to notify the rest of the world?

Anxious, I called the consulate general of Antigua in New York and asked to speak with the tourism representative. I told her everything, about my arrival and the prime minister’s office and how everybody on the island, officials and guests alike, suggested that I was the target of an international mishap involving the Libyans. The woman was silent for a few long moments. She knew nothing of the Mossad, she finally said, but was quite certain that Israelis had always required a visa to visit Antigua. But there was no way, she added, that anyone in Antigua would ever allow me in without stamping my passport, Israeli or otherwise.

I thanked her, hung up, and thought of the marlin.

Postscript: Further investigations show that the Consulate representative was right: Israelis have always needed a visa to visit Antigua. So, it turns out, have Libyans.