PCR tests are largely false positives if you use the ridiculous number of cycles the UK generally uses (45). I won't go too much into the science, but basically each cycle doubles the amount of material and at 15 cycles everything tests negative and at 60 everything tests positive. PCR was never intended to be used for diagnostic work, it was more about general research into confirmed cases (of any disease).
England already had confirmed false positives during the South African tour. But I assume they've repeatedly checked with Moeen to avoid a repeat of that situation. I don't know why they're still using PCR, given the money slushing around in English cricket I'd have thought they'd be using lateral flow tests (LFT), which are more accurate and don't require being sent to a lab. Maybe they're just using PCR as an initial test until it coughs up a positive result, and then they confirm with LFT.
Anyway I didn't want to see Moeen playing anyway, been given far too many chances over the past 2-3 years.
This isn't a case of false positives, that has already been made clear.