If somebody makes a statement of fact saying a certain person sent him an email and gives exact strings from that email, merely saying "That was not in the text of my email" will hardly be a legal problem.

I would have agreed with you if the statement was a subjective one such as "The CEO of the company was being racist or was biased because of my gender". Refuting such a thing is hard and you may inadvertently say something that hurts you later but this is not such a case.

Also, she hasn't quite been silent. She clarified the amount due on this thread (unless you want me to believe that was a part of some grand conspiracy). A similar clarification on the content of the emails could have been made if that guy made those lines up.