As far as I am aware, the Real-time Reverse Transcription-Polymerase Chain Reaction (rRT-PCR) for SARS-CoV-2, Covid-19, is used, or has been used, as a diagnostic tool in Australia, and across the West, although the CDC has moved beyond it because of the prevalence of false positives. Here are some extracts from a peer-reviewed paper detailing this problem. The paper dates from October 13, 2020, so the authorities must have known of the existence of this false positive problem for some time.

https://www.aacc.org/science-and-research/scientific-shorts/2020/false-positive-results-in-real-time-reverse-transcription-polymeras

“False Positive Results in Real-time Reverse Transcription-Polymerase Chain Reaction (rRT-PCR) for SARS-CoV-2?”

“Author: Stanley S. Levinson, Ph.D., DABCC  // Date: OCT.13.2020  // Source: Scientific

 … Among others, false positives will depend on the length of the DNA probes, how many and which genes are measured and technical errors. The DNA probes used in the CDC rRT-PCR test kits for SARS-CoV-2 assay are only about 25 bases long which does not meet the FDA recommendation for nucleic acid-based molecular diagnostics for viral disease infections where 100 contiguous bases is desirable (1). Various methods use different genes and different probes that may not be equivalent. There is a 100-fold difference in limit of detection (LoD) between some assays (2). Technical error, especially due to contamination may cause false positives. Seventy-seven professional baseball major league players initially tested positive in one lab but negative elsewhere (3) in what was deemed Lab error. Except that they had multiple sources for testing, they might have been classified as asymptomatic. We don’t know how many other persons were classified in error from this incident.

Originally, PCR was followed by a second step where a separation technique such as a blotting method was used to confirm that the amplified substance was correct. rRT-PCR is usually not followed by a second step. RRT-PCR is usually applied for diagnostic purposes, not for screening. For acute viral infections, after symptoms appear, a rRT-PCR test battery may be performed. In diagnostic testing, symptoms or high-risk behavior cause an increase in prevalence because those with certain symptoms are classified into characterized groups and false positives are few. …

For SARS-CoV-2 rRT-PCR, cycle threshold (Ct) of 24 or less has been shown to be highly predictable for identifying active COVID-19 cases (4), but since LoD of various methods drastically differ it is unclear which methods this applies to. Generally, methods do not amplify more than 40 cycles, but some systems go beyond 40 Ct. It seems likely that short probes in such systems could lead to amplification errors. Although there is no wide spread EQA proficiency programs for SARS-CoV-2, there is one report (5), of EQA in clinical laboratories for other RNA virus. The authors compiled 43 EQAs of rRT-PCR assays, conducted between 2004-2019. Each EQA involved between three and 174 laboratories, which together provided results for 4,113 blind panels containing 10,538 negative samples. 336 of the 10,538 negative samples (3.2%) were reported as positive. The authors defined the lowest percentage of the interquartile range which was 0.8% as a conservative estimate of the false positive rate. In another report, Sin Hang Lee found that 3 of 10 positive proficiency samples in the State of Connecticut were negative containing no SARS-CoV-2 RNA by a confirmatory assay (1). The Foundation for Innovative New Diagnostics (FIND) examined 22 rRT-SARS-CoV-2 diagnostic tests (6) and found diagnostic specificities ranging between 100% and 96% for 100 specimens assayed by each test. Although the great majority showed 100% specificity, given the small number assayed, the lower 95% confidence limit which was 95% for almost all assays would seem to be a better estimate (possible 5% error). Moreover, these were tested under controlled conditions, not at all similar to high output clinical laboratories running thousands of tests.

The Reverend Thomas Bayes (1701-1761) recognized a kind of statistic that predicts the posterior probability from the prior probability. For testing, this means the post test probability can be derived from the pretest probability if the prevalence is known. This sounds complicated but actually, Bayesian statistics are simple compared to classical frequentist statistics since one does not have to apply a null hypothesis, nor interpret p-values or effect-size and the results are obtained from simple mathematics. If, as discussed above (5), a 0.8% false positive rate is correct, at a six percent positive rate that some States claim, then there would be: 100 x 0.06 = 6 positives/100 tests. But if 0.8% are false positives, then only 5.2% are true positives with a positive predictive value (True positives/total positives x 100) of 5.2/6 x 100 = 86.6%. This means about 13.4% are false positive. Notice as the prevalence of disease decreases, the percentage of false positives to total positives increases because the true positive percentage decreases but the percent false positive (in this case 0.8%) stays the same. Thus, the percentage of false positives would be about 26.6% at a three percent positive rate.

... I conclude it is likely that at current active disease prevalence the positive rRT-PCR results of many “asymptomatic” persons are false positives.