Pointless pedantry, just because I've been watching TWiV: the PCR test is detecting virus RNA because coronaviruses have RNA, and there's no DNA there. The rest I absolutely agree with.
More pointless pedantry from TViV, as I listen frequently as well: the hosts always point out that RT-PCR tests for the presence of viral RNA, but viral RNA particles being inside your nose or mouth doesn't necessarily mean they are infectious. The scale of CT values is 0–100 and lower CT values means more RNA copies. This is used a proxy for infectivity, though it's not terribly scientific. Furthermore, CT values are rarely (if ever) included on the test results.