The non-invasive followup for people with positive test results would knock out a lot of the false-positives. At least, thats what I understand of "the usual result of a positive test result for a serious illness, is that a repeat test does not confirm it"

That said, at what level of risk of follow up diagnostic would you baulk? Any procedure which requires a general is bad news, and if you are over 70 its a lot more bad.