Thanks! Rocco might have had a particular state in mind when he made that claim. 35-40 is bad enough, though, and does give the contrast to 28.

Edit:

The Tweet has a reply saying that Rocco misrepresented the CDC page linked above for PCR tests of vaccinated people.

"That's not what the document states. Wonder if you even read it. I'm a fan of yours but the 28 cycles is for sequencing of the genome this is not to determine positivity. Sequencing is a different process unrelated to positive testing. Be better than this Rocco."

https://twitter.com/CliffKYYJ/status/1388273900203638787

Comparing the CDC page and the Tennessee page that you provided, this Twitter commentator seems to be wrong (i.e., Rocco had it right).

CDC document:

Clinical specimens for sequencing should have an RT-PCR Ct value ≤28

Tennessee document:

Most RT-PCR tests use Ct cutoffs of 35-40 cycles, so any sample with a Ct value below the cutoff, would be considered a true positive

Ct values and cutoffs differ by test and thus cannot be compared from one test to another. A specimen with a Ct=36 may be considered positive by one test but produce a different Ct value and be considered negative or indeterminate on another.