As the video sort of explained a while back the PCR test can pick up anything, it's really not a false positive, the test picked up covid. The critical question as the Fauci Vid questions is how much Covid then makes one infectious, this is something that has been debated a bit. Generally it's not just how much but live/dead and where it's located. Live virus found in the respiratory system makes one definitely more contagious than dead virus in your intestine.
Re using Case numbers for lockdowns, there is really no other way. There is nothing else we know of that's fast enough to stay ahead of the virus, even then using case numbers is lagging it seems.