There’s a naive equation for herd immunity which takes the unmitigated transmission rate or R0 of ~3 and calculates 1 - 1/R0 = .66.
This is the upper limit on the threshold (what I call the “naive herd immunity rate”) assuming there are no unaccounted for effects which would otherwise reduce R0.
Improved personal hygiene, social distancing, PPE, contact tracing, are all various behavioral ways that we have reduced the transmission rate below 2, which reduces the herd immunity needed to get transmission below 1 as long as those measures persist. Another way to say this is that if social measures get us to 1.3 then the infection still spreads until ~25% are infected.
The natural immunity discussed in the article is effectively a free boost to your current herd immunity rate. If serological studies show 20% had been infected, but then you can add another 30% on top of that, you are effectively already at 50% herd immunity.
I’m not sure what you mean by starting from a happy assumption. The real world data shows us that there is irrefutably something working to either reduce R0 or effectively boost the herd immunity level which isn’t showing up in the serological studies. TFA refers to several studies which show scientific evidence of a biological process that can explain what’s happening in the real world.
We can accurately estimate the Rt by just looking at positivity rates, test count, and positive case count. Either R0 is much lower than initially calculated, or effective immunity level is higher than serology tests have shown. I suppose you can pick one, but Sweden at least is a strong datapoint that it’s a function of immunity not social suppression measures.