You misunderstand the problem with PCR tests. The problem isn't false positives in the sense you didn't have COVID, the problem is that you still test positive for weeks or months after you had it. PCR tests are bad for determining whether you are contagious, but they are good for determining the total count of cases. If you had an asymptomatic or small COVID cases, it is still a case, and lucky for that person, now have immunity.
NYS counts probables and repeat positives of the same patient as new cases.
So do other states.
The stats are crap.