The terrible press for GM keeps coming. The New York Times reported this week that GM lied to grieving families about the reasons for their loved ones’ deaths and even aggressively threatened families should they sue the company. This comes on top of recent revelations that GM officials knew about the faulty and deadly ignition switch issue in the Chevy Cobalt for years before recalling the cars. All this hits only months into Mary Barra’s tenure as CEO. While GM’s crisis is dramatic and specific, the crisis and the way Barra is handling it offer a broad array of lessons and a fair dose of controversy about what good leadership looks like and how some in the media judge male and female leaders differently.

Barra has wisely opted to “own” the crisis — even though she’s only been CEO a short while and had no apparent role in the scandal. Nevertheless, she has taken on the crisis with full attention and focus, constantly facing both the media and her own employees with candor and honesty in the process. She has won well-deserved praise for her swift action and willingness to be accountable. But in an opinion piece in USA Today this week, Michael Wolff argues that Barra’s willingness to take responsibility for a crisis that was not of her making shows poor leadership and a female proclivity to seek the spotlight.

Wolff starts by criticizing Barra’s leadership in the crisis. He writes, “Barra could have personally sidestepped this. She’s only been the CEO for two months — it didn’t happen on her watch. And, anyway, CEOs assign responsibility, they don’t assume it.” By taking on this crisis, he argues, Barra defines her legacy from minute one with crisis not of her own making. It’s not clear what he believes she should have done differently, but it doesn’t stop him from writing a poor argument.

In 2010, I coauthored a study with the Center for Talent Innovation that aimed to quantify the intangibles of leadership: the ways in which individuals demonstrate their leadership and inspire others through some universal principles including gravitas, communications, and appearance. We found that leaders must demonstrate three key attributes in order to be seen as a true leader, both to their teams and to the outside world. First, they must have “grace under fire” — the ability to stay calm and coolheaded in any crisis. Indeed, this calm emerged as fundamental to leader credibility. But also, our research found that leaders must stand for and by a clear set of values which define them. Finally, they must have integrity, constantly speaking truthfully. Fundamentally, it emerged that in this day and age, crises are inevitable but leaders are made by the way they handle them.

By taking responsibility, demonstrating her values, and speaking honestly and forthrightly, Barra has shown stronger, not weaker leadership. Had she not done this, or simply blamed others as Wolff argues she should have, she would have inevitably faced withering and justified criticism. A different but recent example illustrates the point.

Chris Christie, in facing the recent scandals around the closing of the George Washington Bridge, refused to acknowledge any role or culpability and blamed a wide range of people from his staff to Port Authority officials. Ultimately, he may indeed be cleared of any wrongdoing. A detailed review he commissioned from a major law firm indicates he may not have had any direct role in the bridge closings as he has argued all along. At this point, though, it almost doesn’t matter. Christie’s passionate refusal to take any responsibility for the actions of his team was a bad miscalculation and made him look weak, self-serving, and desperate. The public has not forgiven him. His approval ratings are at an all-time low, and his national aspirations are clearly unattainable. Had Barra followed Wolff’s guidance and the Christie model, she would have permanently damaged her reputation, credibility, and legacy.

Perhaps the most misguided argument from Wolff asserts that Barra is “part of a new fashion of women running major companies who are, suspiciously, media-willing and comfortable.” In Wolff’s view, Barra speaks honestly to the media only to make herself a star. He points to both Sheryl Sandberg and Marissa Mayer as examples of women who seem to value the spotlight over company success. The reality today is that CEO personal brand is inseparable from the company’s brand and reputation. Take Mark Zuckerberg, Bill Gates, Jamie Dimon — all leaders whose media personae are inseparable from the brands of their companies. The willingness of CEOs to build a strong and clear media presence is not female or self-serving — it’s essential. No one criticized Brady Dougan for his willingness to take responsibility for the illegal behavior of a few employees. In fact, he told employees, “While employee misconduct violated our policies, and was unknown to our executive management, we accept responsibility for and deeply regret these employees’ actions.” Dougan was right to do this, and so is Barra. Speaking with the media about it is part of her job — not some distinctively female desire to be a star.

It’s not uncommon to find that women leaders face some blatant bias and double standards in the media, but it’s worth the effort to call it out when it happens. In an era where so few women occupy top jobs, and many more are dissuaded from taking them for fear of intense scrutiny and bias, Wolff and other writers would do well to reflect more seriously on the true meaning, value, and actions of leadership before leveling criticism.

This blog first appeared on Harvard Business Review on 3/26/2014.

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