You're right. The company should have practiced a little rationality instead of instantly reacting. But she should be held responsible above all because she took offense to a joke instead of taking it to superiors or confronting the guy, she posted it for all to see and read. Her actions did lead to his firing regardless of the company's questionable decision. You don't publicly humiliate someone for something so small. If he had been sexist or made a sexist joke to her or to someone else around then I would understand the company taking action, but I still wouldn't condone the public humiliation unless it was very egregious.