[T-hawk]

PCR is very unlikely to give a false positive if you never had the virus. The viral RNA simply isn't present to be detected. A false positive from PCR most likely came from contamination of the test materials.

PCR is quite likely to give a false positive if you previously had the virus but have recovered, including asymptomatic cases. There are still pieces of viral RNA that can be detected by PCR, even if they're inactivated by having destroyed the viral coating and you're no longer contagious.

So PCR is pretty accurate at saying if you ever had the virus, but not so accurate at saying if you currently have it at contagious levels.