I think there are too many variables to look at it that simply.
The explanations that I have heard that make the most sense is that the high incidence of PCR test positives are due to the cycle threshold (CT) being set too high (this is what causes amplification or replication. The PCR process cracks in half the DNA/RNA/Gene being processed, then it is mirrored (creating two from one), the process is then repeated several times to create multiple replicants, so the math looks like 2^N. The CDC recommends 35 cycles, Fauci recommended not going over 30, but appeared to believe 25 was quite sufficient (a statement he made at a conference in the June/July time-frame), because more amplification than that was as likely or more likely to make something insignificant seem significant (i.e a false positive).
2^25 = 33,554,432 replicates
2^30 = 1,073,741,824 replicates
2^35 = 34,359,738,368 replicates
2^55 = 36,028,797,018,963,968 replicates
2^60 = 1,152,921,504,606,846,976 replicates
Apparently Quest and Labcorp are the two main labs performing the tests and they recommend running the CT up to 55 or 60 (hence the numbers being included above). This statement is based on an FR post I read a few weeks ago where the poster challenged people to go look for themselves at the info the companies provide for guidance. I’ll see if I can locate the post.
Also remember, everything in the sample is getting replicated.
July 16, 2020
4:06 Q: Can we use a cutoff of viral loads determined by PCR to say "This patient is no longer infectious, can go home, can go to a nursing facility. Because right now the physicians are really having a hard time with that."
4:20 Fauci Answer: Again, a good question. What is now sort of evolving into a bit of a standard, that if you get a cycle threshold of 35 or more the chances of it being replication competent are miniscule. We have patients, it's very frustrating for the patients and the physicians...Somebody comes in and they repeat their PCR and it's like 37 cycle threshold. You can almost can never culture virus from a 37 threshold cycle. So I think if somebody comes in with a 37, 38, even 36, you gotta say it's just dead nucleotides period.
4:12 Question: Because, as you know, we can't easily culture infectious virus. You don't have a BSL 3 lab everywhere.
5:30 Fauci Answer: When someone comes in and it's positive they don't give them the threshold until you go back and ask for it.
Some discussion about the labs in Kansas:
Kansas labs set cycle thresholds too high, detect non-contagious virus
Some really heady reading for you:
SARS-CoV2 Testing: The Limit of Detection Matters