[3dee]

As far as I know it does not detect DNA but RNA. RNA degrades slowly and it is estimated it can take 1 to 3 months to be completely gone.

[nyokodo]

You are correct since they use RT-PCR specifically for SARS-CoV-2. However, the number of cycles used in the process is key, <= 24 cycles produces very few false positives for active infection. The OPs explanation for the increased rate doesn’t match this fact.