From the NYT article they're making an argument that 40 cycles can identify too small of a viral load to the point that the person isn't really sick or able to infect others. One of the people quoted said that people identified as positive at 40 cycles should be contact traced. There were really a few arguments in the NYT piece. One was that more testing needed to be done using rapid tests rather PCR which was tied in to PCR being too sensitive at 40 cycles and too slow in a situation where a virus was spreading rapidly. But saying "85-90% wouldn't have been positive if we used 30 cycles as the threshold" isn't the same as saying "90% of PCR tests were false positive"
Here's a decent read with lots of links about PCR testing cycle thresholds and their importance.
https://www.usatoday.com/story/news/factcheck/2021/02/11/fact-check-post-distorts-whos-covid-19-pcr-testing-guidelines/4340677001/
From the link: " But including CT values is not entirely clear cut. Dr. Matthew Binnicker, a professor of laboratory medicine and pathology at the Mayo Clinic, told FactCheck.org that taking high PCR cycle values, or low-positive PCR results, as indicating someone is no longer infectious may miss someone who has "only recently became infected and has yet to hit peak infectiousness. He also clarified "the quality and type of sample can also affect how many cycles are needed to detect the virus, so it's not always the case that a high-cycle result means a person is harboring remnants or only small amounts of the virus,"