The numbers do make sense, you are not understanding what is actually being said.
Mass has done 162,000 tests, 38,000 confirmed cases. That's 23% positive rate. But that's a different test than the antibody test. That test is a reverse transcription polymerase chain reaction, or RT-PCR, where genetic material from a sample is copied and then compared to the genetic sequence of the virus you’re trying to detect.
It's the antibody (blood) test that tells is you've had covid-19 in the past. Serological tests rely on detecting antibodies in a blood sample, usually obtained through a simple finger prick.
When you’re exposed to the virus, your body develops antibodies, which can take several days to over a week. Antibodies are proteins your body makes when mounting a response against invading germs.
Since the vast majority of Covid-19 cases are mild, most people don't even know if they've had it, The fact that a random serological test on the street indicates that over 30% of the people in boston have had covid-19.
The numbers make sense. You're just not grasping what the numbers mean.