Yeah, I wouldn't go so far as to say that this means they're at fault and they've messed up just because of what they said, but I do think it's hurting them more than its helping.
As mentioned - yes, this very well could be a legit problem! I don't mean to dismiss this employees' claims lightly. With the person Musk is though, I bet he sees it as a petty "human" distraction towards getting his larger goals for humanity. That doesn't excuse the way he handles it, but just gives perspective on his response. He seems to be a little bit of a robot sometimes - I don't think human empathy is his strong suit.
I agree attacking women or anyone is stupid in general. Instead, hear the person out and promise to investigate. Then take action if necessary and if not, share the facts. I don't think anyone can disagree with that course of action but hotter heads prevail sometimes on short notice like this.