“Too good to check!” reporters sometimes joke when they hear a story so fantastic they fear checking it out, lest it turn out untrue.

Likewise, the public seems determined to cling to the story that J. Edgar Hoover, the piranha-jawed director of the FBI for over 40 years, liked to par-tay in a cocktail dress, fishnet stockings, full makeup and a wig.

No matter that it’s almost certainly untrue, based as it is on a single discredited source, according to almost every historian of the FBI, including the G-man’s fiercest critics.

With the opening last week of “J. Edgar,” however, the transvestite legend is likely to get fresh legs. While the movie sidesteps any reference to cross-dressing parties the G-man is alleged to have attended, it does include a poignant scene of a deeply grieving Hoover caressing, then donning, his just-deceased mother’s necklace and dress.

Why the obsession with Hoover in a dress?

It’s “the sheer snicker-inducing incongruity of the visual . . . the delicious irony in the spectacle of the man who kept everyone else’s secrets having such a transgressive one of his own,” says Thomas Doherty, a Brandeis University professor and author of “Cold War, Cool Medium: Television, McCarthyism, and American Culture.”

The legend took root in 1993, with publication of “Official and Confidential: The Secret Life of J. Edgar Hoover,” by Irish journalist Anthony Summers. Summers’s principal source was socialite Susan Rosenstiel, the embittered former wife of millionaire bootlegger and distiller Lewis Rosenstiel, a Hoover crony who was bisexual himself.

Susan Rosenstiel had been “trying to peddle this story for years,” Peter Maas, the late organized crime chronicler, wrote in Esquire.

“She had an interest in discrediting her former husband,” Marquette University historian Athan Theoharis, author of several authoritative works on the FBI, said in an e-mail.

What lent credence to the legend was the G-man’s widely known relationship with Clyde Tolson, his elegant longtime aide, with whom he had a spouse-like, but perhaps unconsummated, relationship.

“They ate lunch together every day and dinner together almost every night. They vacationed together, staying in adjoining rooms, and they took adoring photos of each other,” writes Ronald Kessler, author of “The Secrets of the FBI” and other books on the bureau. But no evidence of sex between them exists, he and other historians point out.

The cross-dressing story is “a fabrication concocted by Susan Rosenstiel, who had served time in prison for perjury,” Kessler wrote, noting that FBI protective agents followed Hoover just about everywhere he went.

If “anything scandalous had happened with the director,” one agent told him, “it would have gone coast to coast within the bureau in 30 minutes.”

Theoharis also doubts that Hoover was gay, much less a transvestite who attended an “orgy” Rosenstiel claimed she witnessed at the Plaza Hotel in New York, hosted by Roy Cohn, top aide to the communist-hunting Sen. Joseph McCarthy of Wisconsin.

Doherty agrees. “I’ve always been suspect of the claims that Hoover held hands with Clyde Tolson,” as shown in the new movie, “or that he would appear in full-on drag,” he said.“It’s just one of those stories that is too good to be true.”

Summers stands by his story, and provided a copy of Rosenstiel’s sworn affidavit. He called the cross-dressing allegation “one passage in a biography of some 600 pages.”

But it was the one that stuck.

Former Washington Post “SpyTalk” blogger Jeff Stein specializes in intelligence issues.