Worry and anxiety and depression have been shown to have negative physical results, no? So if you are prone to those psychological reactions, being informed of risks you weren't aware of could literally make you less healthy, even if that particular risk never happens.

It's not universal by any means, but it would certainly affect a nonzero number of people.

edit for anecdata: I know someone who has this reaction, and trouble grokking statistics and risks (gets it intellectually, but has trouble internalizing), so being informed of their risk factor for a given condition can cause them to become consumed with anxiety and worry for a time.