If NFL Commissioner Roger Goodell is going to be toppled, like Richard Nixon, it’s going to be because of a cover-up, and not the original, venal crime itself. And once again, there’s a tape recording at the center of the storm, with a corrupt leader ducking for cover as his lies are exposed almost as quickly as he can sling them.

Goodell has declared repeatedly that no one in the league office had ever seen the second tape from inside the casino elevator, the one in which Ray Rice brutally knocked out his future wife. Even if Goodell’s claim stretched the boundaries of credulity, there was a legal underpinning. The New Jersey state prosecutors are forbidden from sharing material in an ongoing investigation, including the entire period that Rice was in a pretrial diversion program.

Of course, that wouldn’t prevent the NFL from asking for the tape from the casino directly. In a memorandum that was sent to the 32 team owners, Goodell addressed that question, stating, “our understanding of New Jersey law is that the casino is prohibited from turning over material to a third party during a law-enforcement proceeding.”

That’s a lie.

TMZ, which has shockingly become the Woodward and Bernstein of this sordid affair, asked Paul Loriquet, the director of communications for the New Jersey attorney general, if Goodell’s interpretation of New Jersey State law is correct. The answer? “No, it’s not illegal.”

There’s more. Early Thursday, the Associated Press reported that the entire statement, that no one had seen the tape, is also false. A police officer sent a DVD copy to the league five months ago. The AP even got a hold of a voicemail from its source confirming its arrival and saying, “You’re right. It’s terrible.”

The report prompted the NFL to double down—or possibly triple or even quadruple; I’m losing track at this point—in its response: “We have no knowledge of this. We are not aware of anyone in our office who possessed or saw the video before it was made public. We will look into it.”

On Thursday evening, ESPN reported: “Ray Rice told NFL commissioner Roger Goodell on June 16 that he punched his then-fiancée in a casino elevator, four sources have told Outside the Lines, an assertion that contradicts Goodell’s statement this week that ‘when we met with Ray Rice and his representatives, it was ambiguous about what actually happened.’”

So not only does Goodell appear to be a Baron Münchausen-level liar, he’s blindingly incompetent, surrounded by phalanx of lickspittles/attorneys willing to rubber-stamp whatever pabulum is rattling around in his authoritarian head.

The NFL has ordered an independent investigation into the matter. It’s not really “independent” given that it’ll be overseen by two owners known to be Goodell’s cronies and headed by a former FBI director, Robert Mueller III, an individual with more than a few financial ties to the league. Odds are they’ll find a low-level functionary to pin the blame on—someone with an office a safe distance away from the commissioner himself. You know, like Nixon tried to shunt responsibility for the break-in on to Liddy, Sturgis, et al.

On the other hand, If the league actually wants to solve the problem, instead of treating it as a particularly thorny public relations issue; if the league had a vested interest in trying to win back a semblance of trust from the 46 percent of their fan base that happens to be female and the unknown percentage of men who are equally repulsed? Here’s one solution: Hire more women and place them in positions of real power.

The NFL’s not the only league that could use a bit more gender diversity. This bit of news may have fallen through the cracks, what with the cavalcade of abhorrent stories emanating from the sports world, but New York Mets COO Jeff Wilpon is being sued by a former executive, Leigh Castergine, the only female vice president in the team’s 52-year history, for alleged sex-based discrimination.

In addition to detailing the apparently systematic and pervasive failings of the Mets’ front office as a whole—which should come as a shock to no one who has paid any attention to the team’s shady finances—the lawsuit alleges that Wilpon was abusive and dismissive of Castergine because he is “old fashioned and thinks (Castergine) should be married before having a baby.”

In the presence of other team officials, he allegedly said, “Don’t touch her belly and don’t ask how she’s doing; she’s not sick, she’s pregnant.” And, “I am as morally opposed to putting an e-cigarette sign in my ballpark as I am to [Castergine] having this baby without being married.”

Castergine spoke with the Mets’ director of human resources and was advised to quit. You can pretty much guess what happened next. She sought legal counsel and suddenly, her job performance was called into question. While on maternity leave, she was fired by email.

You can draw a pretty straight line between the NFL’s arrogant, unblinking response to Ray Rice in particular and domestic violence as a whole, and the retrograde, macho environment in the Mets’ front office. As David Roth writes at SB Nation, “It’s a locker room culture, at least in terms of the atmosphere of bro’ed-out exclusiveness and meatheaded norms, but this locker room is full of pissy old guys sitting around some diner, clucking endlessly about their nieces...whose workplace brutishness would inspire facepalms at Sterling Cooper Draper Price.”

If you think that this is just one team, a bad apple, or the exception that proves the rule, well then, maybe you too can work in the NFL’s PR department. I hear they could use the help, especially if you’re willing to toe the corporate line without blanching at the bone-jarring inconsistencies and outright falsehoods.

A woman stands a far better chance of figuring out both a disciplinary process and a means of education, intervention, and outreach because women understand the degree to which domestic violence plagues the country in a way that most men just can’t.

I am not in any way suggesting that women are of higher moral fiber than men, but there’s a difference between decrying the horror of abuse and actually fearing it, armed with the knowledge that one-quarter of all women in America will be a victim of domestic violence in their lifetime, and 1.3 million every year—a statistic that doesn’t include the incalculable number of unreported cases.

A woman would not have spent decades ignoring or sweeping the issue under the NFL’s voluminous rug. She’d know that while NFL players as a whole average fewer arrests than the national average, “there are 83 domestic violence arrests, making it by far the NFL’s worst category... relative to the income level (top 1 percent) and poverty rate (0 percent) of NFL players, the domestic violence arrest rate is downright extraordinary.”

A woman also would know that in domestic violence cases, you never interview the abuser and the victim in the same room, as Goodell did with Ray and Janay Rice, because the victim is under far greater pressure to support the abuser’s exculpatory “explanation.” Nor would a woman walk away from that interview believing that Janay Rice “had become unconscious because she had fallen during the scuffle.”

Furthermore, a woman might even have the testicular fortitude to deal with the fact that there’s a link between traumatic brain injury and personality change, mood swings, and domestic violence.

Yes, sports are a male-dominated industry. But there’s no reason for the owners to treat the Patriots any differently than they would Pepsi, or hold the Falcons to a lower standard than Ford. And yes, I’m aware that women still lag well behind their y-chromosome’d counterparts in many, many other industries, but it’s a particular issue for the four major U.S. sports leagues.

The NFL received a C+ for gender hiring practices for team professional administrators and the league office in the most recent Racial and Gender Report Card from The Institute for Diversity and Ethics in Sport (TIDES), but its D- for senior administrators is far more damning. Overall, as Robert McLeod wrote in the Toronto Globe and Mail, women hold approximately 2 percent of the key management positions in the NFL, NBA, NHL, and Major League Baseball.

Why? Well, it’s pretty self-explanatory. There are some pretty archaic, long-held biases and prejudices that remain in place (see Mets, New York). As Sue Rodin, the founder and national president of WISE (Women in Sports & Events) explained in the same piece: “There’s been a cultural mindset, much like it used to be in male dominated industries like banking or financial services, where it’s mostly men you see at the helm. So with sports, it will take some time. Some progress has been made but we’re not at any sort of tipping point, that’s for darn sure.”

So let’s get the ball rolling, if only because a woman would have realized a long time ago, before the slap-on-the-wrist suspension, before the second tape was leaked, and before Goodell was sent frantically running around like Mickey Mouse in Fantasia, trying to keep up with the ever-multiplying swarm of lies, and certainly before 5 p.m. Thursday that the league might want to make some changes to the pregame show and find someone other than Rihanna to sing “Run This Town” to kick off Thursday night’s Steelers-Ravens game.

Take the lyrics literally, NFL. Hire more women to run your town.