I still assume overall the numbers are exaggerated by more than 10x.

Here is my description of the false positive PCR problem:

PCR uses amplification cycles of changing temperatures. These allow the binding of primer DNA, as guides, then warming to enhance the activity of the enzyme that copies that segment of nucleotides.

Lower number of cycles = fewer rounds of amplification = better accuracy.

Higher number of cycles = more rounds of amplification = more error.

It’s like the children’s game “telephone” where each step introduces the (chance) of variation / error. This is compounded by “off target” amplification of other sequences that have some similarity. PCR over 30-35 cycles is garbage, especially if the starting sample is dirty. The starting samples in question are snot.