Navy SEALs, the US military’s premier Special Forces commandos, operate in the shadows of global conflict. Part of their mystique is they don’t brag about, or even discuss, their exploits outside official channels. A critical tenet of the organization’s ethos is: “I do not advertise the nature of my work, nor seek recognition for my actions.”

Most famously, members of SEAL Team Six killed Osama bin Laden in a daring raid in Pakistan in 2011. Since then, speculation has centered on who among that elite team actually killed the world’s most notorious terrorist.

Several team members have detailed some of the action that night in Mr. bin Laden’s compound. Matt Bissonnette wrote the best-seller “No Easy Day” under the pseudonym “Mark Owen.” Others have consulted for filmmakers and video game designers.

Team member Robert O’Neill, the apparent subject of a long piece in Esquire titled “The Shooter,” appeared on a two-part Fox News special and has gone on the paid speaking circuit.

Now, Mr. O’Neill may be in trouble with the Navy – not so much for his apparent claim to have fired the fatal shot (more than one SEAL shot bin Laden) – but for revealing classified details about the operation.

In a statement to several news sources Tuesday, a Navy spokesman said: “The Naval Criminal Investigative Service (NCIS) is in receipt of an allegation that Mr. O’Neill may have revealed classified information to persons not authorized to receive such information. In response, NCIS has initiated an investigation to determine the merit of the allegations.”

O’Neill has not responded to this latest twist in his story, but some of his defenders have.

“In normal circumstances, the Navy would be right to pursue an investigation but there’s still no evidence that a disclosure of any type occurred,” Joe Kasper, chief of staff for Rep. Duncan Hunter (R) of California and a Marine Corps reservist who knows O’Neill, told The Daily Beast. “Regardless of whether you think Rob O’Neill should have identified himself or not, an investigation will to need turn up credible evidence that disclosures were made – and on that front, at least so far, there’s no compelling evidence that occurred.”

Still, there’s no doubt that the top of the Navy’s SEAL command frowns on the kind of publicity O’Neill has generated.

In a letter last month, the admiral and senior enlisted man who runs the United States Naval Special Warfare Command took aim at O’Neill, Bissonnette, and any other SEAL who may be thinking about publicly discussing their exploits.

“Violators of our Ethos are neither teammates in good standing, nor Teammates who represent Naval Special Warfare,” Rear Adm. Brian Losey and Force Master Chief Michael Magaraci wrote. “We do not abide willful or selfish disregard for our core values in return for public notoriety and financial gain, which only diminishes otherwise honorable service, courage and sacrifice.”

That message was brought home to Mr. Bissonnette, whose book was not vetted by the Pentagon before it was published.

Bissonnette has agreed as part of a negotiated settlement to forfeit to the US government most of the income he has received from the book, along with future income. It said the payment to the government has already exceeded $4.5 million. In November, he sued his former lawyers for malpractice, saying they gave him bad advice that tarnished his reputation, cost him his security clearance, and caused him to surrender much of his book's income to the government.

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As for O’Neill, there’s no doubt that he accumulated an impressive military record.

“In total he was deployed on more than a dozen tours of duty in active combat, in four different war zones, including Iraq and Afghanistan. In the course of those tours he undertook more than 400 separate combat missions,” reports the British newspaper Daily Mail. “He was decorated 52 times, leaving as senior chief petty officer. His decorations include two Silver Stars, four Bronze Stars with Valor, a Joint Service Commendation Medal with Valor, three Presidential Unit citations, and two Navy/Marine Corps Commendations with Valor.”