Here's how it turned out
They did an antibody testing study of New Yorkers. They surveyed 3000 people, randomly and found 13.9% tested positive for antibodies. In New York City that rose to 21.2% in New York City but just 3.6% in less-populated regions.
Governor Cuomo noted that the people they tested were out shopping, so it's not necessarily a random sample. The argument is that the people were more likely to be out and not staying home, so they'd also be more likely to have it.
There is also some skepticism about antibody tests. Yesterday this is what the CEO of pharma giant Roche said:
"It's a disaster. These tests are not worth anything, or have very little use," Schwan told reporters on a conference call on the Basel-based company's first-quarter results. "Some of these companies, I tell you, this is ethically very questionable to get out with this stuff."
I think it's clear that more people have the virus than have been tested but whether it's 20% of all people or 3%, that's still nowhere near herd immunity. However it does mean that it's much less deadly.
Back of envelop, 13.9% of New York State's population is 2.7 million and deaths so far have been 15,740. That's just 0.58%. Now you have to assume that many of the people who already have it will get it. I expect that just among those infected, confirmed already or uncounted is 25,000 so that gets to almost 1%. In any case, that's still great news but if the data is right, I don't know if that's going to be good enough for anyone to simply re-open, let alone reports of long-term lung damage even for 'mild' cases.