The problem seems that the analysis and the actors is they don't understand that there will be outliers. Not everyone will do the right thing and it does not take many not doing the right thing to muck things up.

We practice a thing called six sigma because we can't afford unlikely events to cause a disaster. When you are betting billions of dollars with each role of the dice 99% positive outcomes is not good enough need to be 99.9 fine. Better yet, 99.99 fine.

Look at it from the point of view of someone who tested positive. They already have the disease, they have nothing to lose, well except that the school might have to close and some of their friends might get sick too.