The false positive rate for the approved nucleic acid amplification tests (NAAT) is likely low. Therefore, a positive test pretty reliably confirms the diagnosis. That feature makes NAAT a good diagnostic test, but a less than optimal screening test. Using NAAT as the confirmation test on people with respiratory symptoms seems like the best use of a limited and expensive resource.
The Chinese experience suggests that in the early stages of the epidemic, a large number of infections were due to asymptomatic or pre-symptomatic individuals infecting several others prior to diagnosis. I have no reason to believe a different dynamic is in play throughout the rest of the world. So, by the time someone rolls up to the drive in testing station and tests positive, they have likely been infectious for several days before that. Locking them down at that point will be helpful in avoiding additional transmission, but that begs the question of how often do you test asymptomatic individuals, knowing that your available test may not do a good job of finding cases with low, but not zero, viral loads?
As shown, a less specific, more sensitive test, like "fever" lends valuable population based information, and can prompt affected individuals and communities to pull the string a bit to see what's going on.
One piece of good news is that serologic testing is coming on line in a research setting. That should help answer a lot of questions as it matures.
V/R