nice overall, but 1 minor correction -- you wrote

"The percentage of people falsely identified as sick is derived from the test's specificity; a test with a specificity of 80 percent will identify one healthy person as sick for every four persons it correctly identifies with the disease."

that's not actually correct; what you should have written is "... will ID one healthy person as sick for every 4 it correctly IDs as healthy."

that's one false positive (FP) for every 4 true negatives (TN).

how many FPs there are for every true positive (TPs, or people with disease) depends on both sensitivity and specificity, and (at least as important) the prevalence of the disease (how many TPs there are compared to how many TNs).

specificity is only measured in people without the disease.  if a test has an extremely high specificity, of 99%, let's say, it will still produce a huge # of FPs if it's done in a population where the prevalence of disease is extremely low.  imagine you apply this fabulous test to a population where only 1 in 10,000 has the disease.  imagine as well that the sensitivity is perfect (something that's never the case, but let's pretend, just to demonstrate the point), so that it correctly IDs that 1 person as true positive (TP).  it's extremely specific, so there's only 1 FP out of every 100 healthy people (which would make it a far better test than just about any i know of in clinical medicine).  

But ... there are 9,999 people without the disease, so even with this super test there's 1 FP in the 1st 100 ... 10 in the first 1,000, and 100 FPs in the group of 10,000.  at the same time, remember that there's only 1 person with the disease, so at the same time as there's that 1 TP, there will also be 100 FPs.  if whenever the test is positive it leads to some further invasive test and/or treatment, it will round up and subject to the risks of such a program 100 people without disease, along with the 1 person with the disease.  even if it did something fabulous in every TP (again, no intervention is ever that good), it would lead to overall harm (at great cost, as well -- for the test itself in 10,000 people, and for the follow-up program in 100, and treating the harmful consequences of the program in however many) if it led to an unnecessary bad outcome in even 2% of the FPs (who had no disease, and could therefore only be harmed, but not benefited, by any testing or intervention).

For your example of 80% specificity (and continuing to imagine a miraculously perfect sensitivity of 100%) there would be 2,000 FPs out of 10,000, so the ratio of healthy people incorrectly cited as sick (FP) to "people correctly identified with the disease" (TP) would be 2,000 to 1 ... rather than 1 to 4 (that you suggested).

Now throw in that a) no test is actually 100% sensitive (real tests miss at least some of those with disease), b) few are remotely close to 99% specific (so real tests produce far more FPs), c) interventions may benefit few if any -- even among those who are TP, for the reasons you mention (in some, the "disease" never would have manifested itself clinically, or on the other hand in some it's already too late to improve anything by the time the screening test is positive), and d) most interventions have substantial risk of harm ... and you can see why screening (doing a test in a whole bunch of people without any sign of disease -- such that few actually have it) ... even though it seems such a good idea ... is so very rarely actually able to do more good than harm!