This isn't my field at all, and in not that smart, so bear with me.
As I understood it, the idea behind that was that there is a difference between epidemic and endemic herd immunity. But its not lower because some of the population is already immune, but rather it has a tendency to blow through certain groups at different rates.
In epidemic setting, susceptibility is not uniformly distributed among the population, and the disease burns through the most susceptible. I think the argument was susceptibility for a novel disease is based on how connected certain groups are, how exposed to other people they are. for example, cab drivers or first responders are significantly more susceptible than say lumberjacks or WFH office workers. Then after that group gets hit hard, it starts to run out of new hosts for an outbreak and it burns out. Just how differently susceptible populations are determines how low or high the herd immunity threshold was. At least based on the formula they created.
The theory made sense to me as a pure amateur/idiot but I never understood why 20% was the result. I think it was solved for based on European experience, but they had significant NPIs. if you look at the model, it was very sensitive to the CV component, which is the estimate for the difference in susceptibility i believe.
Here is the pre print if you want to read more.
https://www.medrxiv.org/content/10.1101/2020.07.23.20160762v3.full-textHere's another one that goes a little further and talks about a transient collective immunity, which i think means a short term barrier but not actual herd immunity, which would let it susceptible to other waves. The reason its short term is because the heterogeneity is assumed to decrease over time as fewer people adhere to guidelines and/or guidelines get lifted. And since the threshold is so sensitive to that, it becomes materially higher, and thereby allows another outbreak to occur. At least that's how I read it. So that would bridge all this, in a way. It predicts even the hardest hit areas would eventually become susceptible to another wave of infections, like we are seeing now.
https://www.medrxiv.org/content/10.1101/2020.07.26.20162420v3.full-textCurious what other thoughts are, especially where I may have misread or misunderstood.