So much for the what-happens-here-stays-here mantra. Sean Payton will not be allowed to coach the Saints in 2012 after word got out about the team’s bounty system. (Patrick Semansky/Associated Press)

The debate around the New Orleans Saints’ pay-for-performance system initially centered around the prevalence of such programs and their propriety within the NFL. But the NFL’s punishments of the team revealed something else: a discord among current and former players not only over the bounty program and the league’s response but in the manner in which they became public.

Some players clearly believe the existence of the bounty system should have remained where it began: in the locker room.

“When all this stuff came out, one of the first things I tweeted about was: Who snitched?” said Damien Woody, an offensive lineman for three teams over a 12-year career who now serves as an analyst for ESPN. “Because as players, we look at ourselves as part of a special fraternity. We go to battle with each other every week. And there’s only 1,600 players in the NFL; that’s not a lot. Guys know each other. Guys have special bonds. It’s a close-knit community, and people expect there to be trust.”

Shortly after the NFL announced the suspensions of Saints head coach Sean Payton, former defensive coordinator Gregg Williams and General Manager Mickey Loomis, those sentiments spilled into Twitter, then onto the airwaves.

Longtime defensive lineman Warren Sapp, now an analyst for the NFL Network, tweeted that he knew the identity of what he referred to as the “snitch” in the case. When a reader suggested the name of tight end Jeremy Shockey, who played with New Orleans from 2008-10, Sapp responded, “Bingo!”

Shockey immediately took to Twitter, and later to interviews, to deny the charge and defend himself. But the idea that revealing such programs is nearly as serious a crime as running them became apparent when the NFL initially announced its investigation into the Saints’ program this month. Shortly thereafter, former New Orleans safety Darren Sharper told a Philadelphia radio station that the revelation “kind of appalls and upsets me.”

“To tell what’s going on inside a room when we’re a family and everything that happens within that room should stay in that room, I’m upset about that,” Sharper said.

When several current and former Redskins spoke with The Post about the existence of Williams’s pay-for-performance system during his tenure as defensive coordinator in Washington from 2004-07, only two would allow their names to be used, and they have since declined further comment.

The what-happens-here-stays-here mantra, though, isn’t embraced by everybody. Minnesota Vikings punter Chris Kluwe, an outspoken voice on a wide range of topics about his sport, profanely admonished “everyone who thinks the source was a ‘snitch’ and a bad person” on Twitter.

“Try doing the right thing for once and standing up for what’s important in life — the proper treatment of your fellow man,” Kluwe wrote while rejecting, among other things, what he considered the “short-sighted, narrow-minded hypocrisy” that allowed players to close ranks.

Some outsiders believe the players’ culture of isolation doesn’t serve them well.

“If we’re thinking about the common good, we’ve got to change our way of thinking,” said Dan Lebowitz, the executive director of Northeastern University’s Sport in Society program. “Maybe, because of this, a whistleblower might no longer be called a ‘snitch,’ but somebody who cares about the collective good of a system. That could be true not only in sport; our culture can be helped by people who stand up and make a statement.”

Lebowitz said the actions of NFL Commissioner Roger Goodell — not just in the Saints’ case, but in dealing with fines and suspensions for unnecessarily violent hits — have set a “tenor for the tenure of Roger Goodell, and that tenor is he’s going to establish a code of conduct for that league.”

But even that assessment engenders debate. Former safety Lawyer Milloy tweeted that “NOBODY is safe under” Goodell’s watch. Former Saints receiver Joe Horn told SiriusXM NFL Radio that Goodell “got too much damn power,” and called for Goodell to look into all 32 NFL teams for similar programs.

“He’s just not a fair commissioner,” Horn said. “All I’m saying is: He’s not fair. If you’re going to do something, do it across the board.”

The league, in the aftermath of the Saints’ case, has told all 32 teams to certify in writing by the end of the month that they do not have a bounty program in operation.

Horn is one of a dozen players who are suing the NFL, alleging teams routinely misused a painkiller before and during games, exacerbating some injuries, including concussions. Woody believes Goodell’s actions in the Saints’ case — a severe response to a practice the league considered dangerous — could inform how the NFL defends itself in such cases.

“Players want player safety,” Woody said. “That’s a concern. . . . When it’s time for both sides to go to court, this particular issue will come up. And then there could be lots of players who might be happier that people know about what went on. You got to look at the bigger picture. At the end of the day, you’re a player. The National Football League is bigger than you.”