This could be an international incident?

Bowman is, of course, American — South Carolinian by birth, a Florida State swimmer in college. He rose to prominence as Michael Phelps’s coach long before the icon was iconic, back when he was a kid in Baltimore, and then through all 23 Olympic gold medals. Bowman served as the head coach for the U.S. swimming team as recently as last summer at the world championships in Fukuoka, Japan, and has been a fixture on American teams, as an assistant or head coach, for two decades.

But at these Paris Olympics, Bowman wears a shirt with a small shield and the word “France” over his heart. His official role is as an assistant coach to the French team. His main job is coaching French megastar Leon Marchand, who began his meet by winning gold in the men’s 400-meter individual medley, a performance in an absolutely delirious La Defense Arena that moved Bowman to tears — just as Phelps’s swims once did.

Phelps had owned the world record in that event since the 2008 Olympics, where he bagged a record seven gold medals. But Bowman is reveling in the idea that a Frenchman not only won gold in what many regard as swimming’s most torturous event — but that the same Frenchman snared the last of Phelps’s world records at last summer’s world championships.

“He’s the best in this event in history,” Bowman said, beaming.

The Olympics brand themselves as an opportunity for the world to come together. But when they do, they fight fiercely against the nations around them. The Games are mostly congenial. They’re also inherently jingoistic.

Take the Australian swimming team. The Dolphins, as they call themselves, embroiled themselves in patriotic controversy last week, before the torch was even lit. Seems one of their assistant coaches, a fella named Michael Palfrey, had the audacity to train a South Korean who reached the Olympics in the 400 IM. And when Palfrey arrived in Paris, he spoke with Korean television about his hopes for Kim Woo-min.

“I really hope he can win,” Palfrey said. He punctuated his remarks with, “Go Korea.”

This was, it seems, a traitorous act Down Under.

“Promoting an athlete who’s not Australian, it’s just … it’s not,” Australian head swimming coach Rohan Taylor said, searching for the right word. And then he found it.

“It’s un-Australian, to be honest,” Taylor said.

The Australian contingent talked about sending Palfrey home. It didn’t. Saturday, on the Olympic meet’s opening night, Kim won bronze — behind one Australian, Elijah Winnington, who took silver, but ahead of another Australian, Sam Short, who finished fourth.

“Very disappointed,” Taylor said. “So disappointed. For a coach on our team to promote another athlete ahead of our athletes is not acceptable. … He was taken to task on it and was very remorseful.”

This seems kind of silly. There are all sorts of examples across these Games — across any Olympics — in which citizens of one country coach athletes from another. The new coach of the U.S. women’s national soccer team is British. The coach of superstar gymnast Simone Biles, an American, is French. The head coach of the U.S. men’s swimming team was born in Trinidad and Tobago and won Olympic gold for Suriname.

The Paris Olympic slogan is “Ouvrons Grand les Jeux” — or “Games Wide Open.” Taken one way, we should be open to ideas from every corner of the globe, be that in culture or in coaching. Seems simple, right?

In swimming, it can be complicated. Which brings us back to Bowman.

The 59-year-old is forever linked to Phelps, whom he started coaching at the North Baltimore Aquatic Club before moving on — first to Michigan, where Phelps trained and attended classes and Bowman became the head coach, and then to Arizona State, where Phelps trained as a professional and Bowman basically built a national title-winning program from scratch.

To become a powerhouse in collegiate swimming, coaches have to recruit internationally. According to the NCAA, there are 223 swimmers at these Olympics who compete or competed at American colleges — 46 who swim for the United States, and 177 who represent 83 other countries. Siobhan Bernadette Haughey swam at Michigan — and has won three medals for her native Hong Kong, one here. Ireland’s Mona McSharry snagged a bronze in the 100 breaststroke here — three months after she posted two runner-up finishes at NCAA championships, swimming for Tennessee. You get the idea.

Frequently, those foreign swimmers remain with their college coaches, who often have second jobs training groups of professional swimmers alongside the kids. Florida swimming coach Anthony Nesty, the head men’s coach for the United States at the Olympics, is responsible for the Gators during the college season. But he’s perhaps better known because he trains gold medalists Katie Ledecky, Caeleb Dressel, Bobby Finke and other Olympians.

So, then, Bowman and Marchand. Three years ago, Marchand reached out to Bowman by email. He ended up at Arizona State, where he won 10 NCAA titles and helped the Sun Devils to the team championship this spring. (Bowman since has accepted the head coaching job at Texas, and Marchand is moving to train with him in Austin.)

But at last year’s world championships, Bowman’s loyalties appeared divided. He was wearing Team USA gear, but the first questions at his news conferences were about a French swimmer. U.S. swimming officials weren’t thrilled that their head coach was openly rooting for one of their competitors.

So by Bowman’s telling, he decided it was best if he recused himself from the American program — and instead coached Marchand, with the French team.

“It just makes it so much better for everyone for me to coach with the French because the French have no stipulations about me coaching other nationalities, and it’s a little different with the USA team, which I certainly respect,” Bowman told reporters when he made the announcement this spring. “So it just makes sense for everybody because I can coach everybody that I’m coaching now.”

That includes American backstroke star Regan Smith. It includes Hungarian Hubert Kos, last year’s world champion in the 200 back. And it includes Marchand — who will go for gold in both the 200 breaststroke and 200 butterfly Wednesday night. He is the swimming star here — and the reason Bowman’s flying a different flag.

“It’s been wonderful,” Bowman said. “The French people have been amazing, and it’s just been great to be a part of this and to be able to help Leon kind of fulfill my promise to him.”

Yeah, the Olympics are about patriotic pride. But they’re also about people and their relationship and commitment to each other. Bob Bowman isn’t committing treason. He’s helping the star of the host nation maximize his outsize potential. Turns out you can bleed two kinds of red, white and blue at once.