When articles like this compare the number of known cases detected with the PCR diagnostic tests with the higher estimate based on antibody testing, they're comparing the sum of all cases detected since the start of PCR coronavirus testing with a point-in-time estimate of the proportion of the population that currently has antibodies for exactly this reason.
FWIW, Queens and Brooklyn (Kings county) are at 50.7% and 48.3% positive tests respectively.
https://covid19tracker.health.ny.gov/views/NYS-COVID19-Track...
Today: Kings 548/1835 = 29.9% and Queens 786/2428 = 32.4%
But as another commenter said, it's not impossible that there are many other people who had infection which is not currently active.
Using the overall test rate doesn't really help, I think.