You can hardly conclude that broadly screening populations are ineffective from this study. You have to consider, among other things, the treatments available for the given disease being screened and the cost of that screening program. If treatments for the disease already have a low success rate (what is low?), the timing of detection doesn't really help. Additionally, if the cost of the screening program is negligible (what is negligible?), then even successfully treating a few patients may be worth it.
The current consensus about over-diagnosis (as I understand it) is that when there is a significant false positive rate and the cost of proving the positive false is high (in money, time, effort, worry), the screening program is not helpful. Some go further to say that low cost screening drives some of the high cost to outcome ratio in the US. I'll try to find a cite in my textbooks if you are interested.
I think the issues are deeper than that of false positives. Its possible that transient diseases get detected that would have fixed themselves without any treatment. Insead of a non-treatment one now has to deal with the side-effects of the interventions applied.
