I think CDC is saying that the rate of false positives can be high relative to the number of positives in a large sample of tests. For example, if 1% of a population has the virus, but the test has a false positive rate of 1%, then 2% of the people tested will get a positive result - those actually positive and the false positives. In this case 50% of the positives are false.
But if 20% of the population actually has the virus, an additional 1% false positive is only 1/21 of the total number of positives (less than 5% of the positives are false positives)
We’re saying the same thing.
Even a low false positive rate gives an exaggerated reading in a population with a low incidence of infection.
But emphasizing this seems misleading, doesn’t it?