Earlier quoted context omitted.
0 out of 100 controls and 6 out of 500 gives a very wide confidence interval. You could easily get those numbers with 1% false positives and no true positives in either group. Is your prior for false positives low enough to rule that out?
They did two independent assays so I would think the false positives rate should be far below 1% - certainly the authors seem to think so. Secondly if they were false positives, I would expect them to be randomly distributed. Not concentrated in the affluent capital city, and not solely in the second cohort with none in the early march cohort (as you would predict if exponential growth is occurring).
Your second two points are fairly compelling.