Your reply looks quite good to us. You are dropping hints about the possibility of miscommunication and she is free to pursue this or not, and will likely not, as she has already concluded in her mind that you fall short. So there is no shame for you in this, she is simply predisposed to her bias as the inaccurate prior knowledge was indeed there first and is the gold standard, so to speak. And your failing to see this, in this case two great truths, causes her to believe you are discerning information of an inauthentic source. So you can do what you wish here, but we would suggest simply sending your general assessment and then letting go of this. As we said, these things may happen from time to time and are unavoidable.