Bowel screening problems throw up issues with mortality too. I was at a recent review of screening at a group of UK hospitals and it was found that the average age of death is the same for those with bowel cancer that were detected by screening, detected by accident, detected after an emergency or detected at autopsy.

A 35% overdiagnosis rate means that for every 3 correct cancer diagnoses made, about one error occurs. That means if the diagnosis is cancer, about 75% of the time it actually is cancer. If the rate of false negatives is small enough, I think I would bet my life on that.

Edit: Sorry, I just noticed that what I wrote seems to imply I disagree with you when, in fact, I agree with you.