They could have defused the controversy almost immediately by identifying the actual cause and fixing it. Part of the reason the story blew up was that DHH and his wife struggled at length to even get an explanation for the problem or find a human who could fix it. The opacity of that whole machine and its resistance to correction is why it became a fuss. I honestly don't care whether it turns out to be about gender, because the end result of that system is that someone got discriminated against in a way that was indistinguishable from being gender discrimination. In the same fashion, if your pricing algorithm accidentally (due to training set bias or whatever) has a 20% higher chance to overcharge people of color, it doesn't really matter how it got that way. It's a racist algorithm and that doesn't mean you're a racist: It just means you have to fix it.
Similarly, if the firings were carefully vetted and legally justified, they could have done a better job of explaining that rationale to the public. As a former Google employee the public rationale was obviously deceptive in some fashion, and undermines any suspicion I might have had regarding the employees in question. I worked with plenty of people at that company who probably deserved to be fired, but when the company behaves that way in public and selects people in a way that coincidentally undermines union organizing, I know who I'm going to suspect.