I wonder why she thinks that. If you agree, will she ask you to side with her in reporting the neighbor with too many cats to the authorities?

Humorous answer first: I'd tell her she's missing out on the love a cat can give. Serious answer, I agree with everyone who said they would just let it go. I'd probably say something like, "Yes, she does have cats." I guess I'd go for the Captain Obvious type of response because I can't think of anything you might say that would satisfy her.