The logical side of me agrees with PPs that you don't owe a response and it could lead to drama.
However, I've been in this situation and I did provide the info my research coughed up because, similar to this situation, her comments were factually wrong. I also think if someone asks, it's fair to respond.
I don't remember the exact wording, but I mentioned I thought it sounded interesting but in researching it, I discovered x, y and z. And when I ended it, I stuck something in there that stated I hoped she found this useful, but if she wanted to discuss it further, I wasn't the person to talk to (or something like that) because I'd learned what I needed to know.
I don't always assume the person is on a mission of some sort. She might really want to know if she missed something, although a lot depends on how she phrased it when she asked you why.