Since the "published papers" cited in the website you mention are NOT peer reviewed, but websites that anyone can "publish" to, there's limited scientific value to this argument. The Clinical Infectious Diseases Correspondence is just that, a letter to the Editor that is not reviewed. However the data are interesting, as it has always been a difficult exercise to equate PCR Cycle Thresholds (Ct) to infectivity.
AAMOF I don't know of ANY instance where the smallest Ct has been resolved to determine the "infectious dose" for ANY virus. "Cutoff" determinations for highly dangerous viruses like COVID-19, HIV, HBV, HCV, etc. are always done on the side of caution. Higher number of cycles with the absence of viral nucleic acids are highly suggestive the person is not infected/infectious. You have to ask yourself this, would you like a unit of blood that has some HIV RNA detected in it after 25 cycles, 30 cycles, 35 cycles, 40 cycles? I sure as hell wouldn't...
And there is a gross error in the text of the article, "And this same test is used for hospitalizations"... NOBODY gets admitted to the hospital solely on a PCR positive result with no extreme and life threatening clinical symptoms. If they did that, the hospitals would have been chock full months ago. All states report "New Positives as determined with PCR, Resolved Patients, Hospitalized Patients Patients in the ICU and Patients on Ventilators. As you go down the last three categories on that list are the smallest, and no where near the "New Positives" number.
If these authors would like to better defend their treatise that high Cts do not correlate to infectivity, a prospective studies following folks with high Cts over a couple of months would answer the question. They could track RT-PCR Cts over that time from swabs, Viral Antigen from swabs, and IgG and IgM results from blood samples, along with basic clinical symptoms. When all these test results are correlated you can start to have a true clinical picture of whether or not the higher Cts are irrelevant from a clinical perspective. Nothing in this package shows these type of data.