NYC had a 20% antibody rate back in April; the disease being under control in NYC may be due to having built up some level of immunity and (sadly) having the vulnerable population die off.
There are small hints that it MIGHT not be possible. The antibody tests measured the infection rate around April 15 or so, the number should be higher now. Second, there is some evidence that a percentage of people don't develop antibodies (only T cells) but are immune. Finally, we don't really know what is required for herd immunity.
None of this is to say you are wrong, just why it MIGHT be possible that NYC cannot have a second spike.
(herd immunity question): https://www.quantamagazine.org/the-tricky-math-of-covid-19-h...
(T cells and immunity) https://www.biorxiv.org/content/10.1101/2020.06.29.174888v1
(peer reviewed article on NYC antibody testing). https://www.sciencedirect.com/science/article/pii/S104727972...
How much more is up for debate. A competent government would be regularly conducting these surveys and publishing the results.
We have been more open, with many protests, streets full of open air bars, etc. for months.
I would bet $100 that NYC, if we could do a full antibody and t-cell assay, would show the majority of the population was infected.
Furthermore, I would submit that R0 as a crude instrument ignores network effects. I'd wager anyone who is a "super spreader" in NYC has been infected at this point.
Some papers have suggested a 20% herd immunity threshold taking into account the network effects. I doubt it's that low, but it is an important factor to consider.
NYC had a 20% antibody rate in a sample of people who were out shopping and consented to giving their blood for the study. That is enough potential sources of bias that assuming the general population had a 20% antibody rate strains credibility.
Sadly, I don't have a link. Hopefully my memory is accurate.