Katie Holmes and Tom Cruise’s split: Is privacy the best policy?

Forget what you might have heard at that Fourth of July barbecue: Katie Holmes wants to keep her divorce from Tom Cruise as private as possible and has not filed for an emergency custody hearing, her attorney said Thursday.

“The reports about an emergent filing last Friday are incorrect. Other than her action for divorce, the only pending application filed by Ms. Holmes remains her request for an anonymous caption,” attorney Jonathan Wolfe told L.A. Now.

Cruise has yet to file any papers, TMZ reported, citing sources who said the actor was likely to file custodial papers in New York first, while requesting that the case be moved to California, largely seen as the couple’s primary state of residence. Holmes filed for divorce June 28 in New York, seeking primary residential and legal custody of their daughter, Suri.

“Anonymous caption” means papers are filed with initials only, or sans names entirely, making the case harder for journalists and other interested parties to track through the court system, attorney Michael Stutman, a New York divorce specialist, told Buzzfeed. But fame doesn’t come with a cloak of invisibility included -- rather, Stutman said, making the names public would have to compromise the safety of the divorcing parties or their children for the anonymity request to be affirmed.

In any case, Holmes’ alleged desire for privacy could be just what the etiquette of the situation calls for, from the divorcing parties as well as the famous folks around them, nationally certified manners expert Lisa Gaché told The Times.

In other words, fellow celebs Will and Jada Smith were on target — “You have to keep it light and breezy,” said the Beverly Hills Manners owner — as they ignored the quote-seeking paparazzi at LAX the other day.

PHOTOS: Tom Cruise and Katie Holmes through the years

Alas, Gaché acknowledged, people who are behaving politely “can sound rather boring” to folks who are looking for more dish on the split.

Witness Katie’s big revelation to the New York Daily News on Wednesday: “I’m all right,” Holmes reportedly said. “Thank you.” ¡Escandalo!

(Wait, really, ¿Escandalo? Um, no, never mind, no scandalo. But very polite, thank you. Not bad for a woman with paparazzi staking out her building, not to mention the Whole Foods.)

But “manners aren’t milquetoast,” Gaché said. “Katie would do well to channel the likes of Grace Kelly and Jackie O,” the latter of whom she recently portrayed in a TV miniseries. Jackie “handled things gracefully, she always had this persona that was poised, put together, and she never let her guard down.”

Though it might not always be possible, that would be the best posture for Holmes to adopt, she said: One where privacy and respect come first for all parties involved, including daughter Suri and the Suri of the future, who will eventually be able to look back on how her parents treated each other during their split.

“Maybe she can channel that poise and ... and maintain her moral compass.”

And if the custody fight were to turn ugly, with one or both parties going off the rails -- and perhaps weaponizing personal information gleaned from Scientology “auditing” sessions? “We cannot control what another person does,” Gaché said, “only the way we respond.”

PHOTOS: Famous Scientologists

News Corp. Chairman Rupert Murdoch went a bit off the reservation over the weekend, commenting on the TomKat divorce in a tweet that could be an unleashing of his journalist hounds to pursue a Scientology angle to the story, or simply a dude sticking his nose into other people’s business.

“Scientology back in news. Very weird cult, but big, big money involved with Tom Cruise either number two or three in hiearchy,” Murdoch tweeted, adding, “Watch Katie Holmes and Scientology story develop. Something creepy, maybe even evil, about these people.”

“What Rupert Murdoch said only did Rupert Murdoch a disservice,” Gaché said, though the media baron might disagree.

“Since Scientology tweet hundreds of attacks,” Murdoch wrote hours after his first blurts. “Expect they will increase and get worse and maybe threatening. Still stick to my story.”

Sources with Team Tom, incidentally, told TMZ on Thursday that the divorce has nothing to do with Scientology, which they said Katie had embraced fully even when her other half was away filming. While not disclosing what the divorce is about, they accused Team Katie of spreading that story line as a way to hurt Cruise.

Not polite.

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