Yeah, that's true.

Let's add in, for the obvious fun, that the rate of asymptomatic infection is lower than the false positive rate of tests.

There may be a misunderstanding about terminology here. COVID-19 is the clinical disease caused by the SARS-CoV-2 virus. If you are infected by the virus but asymptomatic then you don't "have Covid".

Covid has become the shorthand for the virus, this was inevitable when the actual virus is being communicated with something like a serial number.

Every infectious disease epidemiologist & physician I know uses "Asymptomatic COVID-19".