In studies of diagnostic test accuracy, the independent variable is the index test result and the dependent variable is the gold standard result. In studies of screening programs, the independent variable is whether the person was screened and the dependent variable is an outcome like survival or mortality. It is rare to do a study of a diagnostic tests where the independent variable is whether the patient received the test and the dependent variable is survival or mortality. Instead, the assumption is that accurately diagnosing the condition will lead to beneficial treatment.
Differential verification bias occurs when a positive index test leads to application of an immediate invasive gold standard and a negative index test leads to using clinical follow-up as the gold standard. This is a problem if some patients would have a positive invasive gold standard but negative clinical follow-up. Call these patients "resolvers". In these resolvers, the index test can't be wrong, so both sensitivity and specificity are biased up relative to a study that used a single gold standard. It is this group of resolvers that brings to mind overdiagnosis, because if they get both the invasive text and clinical follow-up, they are classified as D+ but their outcomes are good.
So now consider a study of a screening test that compares outcomes only in the D+ patients, some of whom are in the screened group and some of whom are in the unscreened group. Both groups will have resolvers, but in the screened group, they will be classified as D+ and included in the denominator over which we put the number of outcomes. In the unscreened group, they will not be classified as D+ and not included in the denominator. The larger denominator in the screened group (due to inclusion of resolvers) leads to a lower proportion with the outcome.
It occurs to me that a simple numerical example where we have 1000 screened and 1000 unscreened with 200 resolvers in each group might make the effect of resolvers on the groups' outcome proportions clear. Maybe next year.