Also, here is the NY Times article.
It's a stunning revelation. The vast majority of positives (in a sample from the NE) basically aren't actionable. The person who tested positive won't get sick and they won't spread to others. Basically, they shouldn't be labeled positive at all.
The conclusion from that article is simply that a huge % people who get a positive result are no longer contagious and don’t need to isolate.
To say "shouldn't have been judged as positive " seems like you are confusing the findings in that article, or have some specific view on what "positive" means. At one time they were able to spread it and were potentially sick.
The pcr test checks viral load. The findings are about checking "viral load" with respect to the current level of infectiousness in the test-taker. This is unrelated to how sick they might be now or in the future, or whether they were a spreader a week ago, it is just related to whether or not they could be a spreader now.
Recall that peak infectiousness is prior to any symptoms, meaning your viral load is highest before you even feel it, then it slowly decreases thereafter.
The average person is PCR positive for about 30 days. But the average person is only infectious for about 7 days (symptomatic or asymptomatic). The data just shows we're catching too many people AFTER that 7 day window.
One reason for testing is to determine the clinical health of the human. PCR is good for this. Another reason is to check infectiousness for the sake of community health & spread and if we're using PCR then the article says we're testing at the wrong times because the window of infectiousness is small, and our tests are either too soon or too late.
For you to conclude "The person who tested positive won't get sick" is wrong, it just means that are probably done spreading.