Some articles about the false positive rate below though I haven't found the one that had that particular mean value. Yes, it depends on where you are, and even more on how prevalent COVID-19 is where you are. A bigger problem (or at least a more significant percentage of wrong results) is false negatives. I did not grab the links but one article suggested near 100% false negative early after an infection and 20% false negative 5 days after infection. Another article suggested current COVID-19 tests result in false negatives 33% of the time on average. I suspect the false negative rate is much lower once you've reached the point of being symptomatic which typically takes 5-6 days but up to 14 days. Various studies (no doubt with various CT values) on false positives seem to suggest a false positive rate of 1 to a few percent. I don't get the impression that the CT values used thus far (up to 40) commonly give false positives so much as they are more likely to detect early infection and recent recovery. True false positives seemed to be most commonly caused by contamination at various points in the testing process (contamination of reagents, contamination during collection, etc.)
https://www.medrxiv.org/content/10.1101/2020.04.26.20080911v1.full.pdf
"Review of external quality assessments revealed false positive rates of 0-16.7%, with an interquartile
range of 0.8-4.0%. Such rates would have large impacts on test data when prevalence is low. Inclusion of
such rates significantly alters four published analyses of population prevalence and asymptomatic ratio. "
https://www.medrxiv.org/content/10.1101/2021.04.06.21255029v2
"Using current data providing by the Public Health England (PHE) as of the most recent complete data, a false positive rate of 1.16% (95% CI 1.09 - 1.23%) was found for the PHE PCR test for the period 1 January through 29 March 2021."
https://theconversation.com/coronavirus-tests-are-pretty-accurate-but-far-from-perfect-136671
The below article explains why different CT values are useful in different scenarios and what a positive result likely means at different CT values. It seems that it actually makes sense to test an asymptomatic person who has had the vaccine at a lower CT value just as it would make sense to test a symptomatic person at much higher values. But yes, you have to be very careful how you compare the results for the purposes of counting infections.
My point is measuring with different CT values is fine as long as the effects of different CT values are understood and taken into account when publishing results. I would think that would be obvious. On the other hand, if you are using results from different CT values and just taking the raw numbers without considering the effect of the different cycle counts, then yes, of course it would be misleading. I'm just saying it isn't automatically misleading. It depends on if and how they account for the difference when reporting the results. Scientific studies (which tend to be published as something a bit longer than a paragraph and include a lot of data you don't necessarily get unless you read the study itself) will probably take these things into account. They usually do. What the media reports and politicians say in their one sentence summaries of such reports may be a completely different story. Often "science" is blamed for being political when it isn't the science so much as how the results are selectively interpreted.
You seem to be suggesting that they shouldn't use different CT values in different circumstances but the above article explains why it is useful to do so. The fact of the matter is that it can make sense to test people at different CT levels based on their circumstances and the purpose of doing so isn't to nefariously make invalid comparisons though of course someone could do that.
Excellent response by the way. I'd give you a higher value vote if I could.