Now that is a useful discussion. The more I think about the study (the article covering it is just sh*), the more I think it would have been better to compare how many people had an actual colonoscopy between the two groups, compare everything that was compared between a) people with invite who did show up and those without invite that showed up b) people with invite who didn't show up vs. those without invite who didn't show up and c) those who showed up vs. those who didn't (the most important question). The latter can then be used to gauge overall usefullness by age brackets, gender, region and so on. Obviously, as soon as there are risk factors or other test results, we talk a different game all together.
As it stands, this study, while statistically very good, doesn't help anything to answer the really important questions and only confuses people by causing discussions about the study methods, then used to derive conclusions about colonoscopies (utter nonsense, but first principle thinking using supporting science /domains is really en vogue at the moment) instead of discussing the usefulness of colonoscopies in increasing survivability, early detection and decreasing probability of colon cancer.