I think it's pretty common to eat milder foods when you are ill. I know I do. If that is universally true, and all else being equal, you could probably simplify this headline down to "getting sick less linked to a longer life."
Reminds me of the Dilbert cartoon (wish I could find it now) where the discussion was on how a survey showed that heathy people exercise more. Wally commented that's because sick people are too sick to exercise.