I’m at a loss to offer any logical comeback that might cause people like this to reconsider their conclusion. When people don’t agree on a common set of facts then arguments aiming to persuade are futile and do more harm than good.
Maybe the best tactic is to express commiseration and extend a sincere offer to help ease her illness. How about this? “What rotten luck! Here, try some of this cinnamon-spiced tea.” (or perhaps some folk-remedy like a hot toddy)