False positive rate, anyone?

If you tested literally every person in the US, you would end up with about a thousand false positives. (This assumes that this is 1987, and we have the second, independent test, rather than just 1985 when we have only the one test.) If you restrict your sample to, say, New York City and San Francisco and so on, then you dramatically lower the number of false positives while still covering a large part of the at-risk population.