These assays are very skewed toward producing false positives. Exactly for this reason. It's not perfect. PCR can miss the early stages of the infection too.

These assays are very skewed toward producing false positives. Exactly for this reason. It's not perfect. PCR can miss the early stages of the infection too. These are just signals. Luckily we know that viral load is the factor for transmission rate (infectiousness). So even if someone is (false) negative, but has symptoms, should self-quarantine.