My apologies for editing my reply to add a third paragraph while you were replying to it, but I think that explains the relevance of the age dependence to this study: the decrease in the prevalence with age suggests that they actually do exacerbate the diseases they are associated with, and so the association is not merely a correlation.

Note that they are not suggesting these genes have been the subject of selection; it is the hypothesized number of such late-acting genes that were not found that are assumed to have been selected against.