Ioannidis corrected for false positives with a point estimate rather than the confidence interval. That's better than not correcting, but not defensible when that's the biggest source of statistical uncertainty in the whole calculation. Obviously true zero can be excluded by other information (people had already tested positive by PCR), but if we want p < 5% in any meaningful sense then his serosurvey provided no new information. I think it was still an interesting and publishable result, but the correct interpretation is something like Figure 1 from Gelman's

https://sites.stat.columbia.edu/gelman/research/unpublished/...

I don't think Gelman walked anything back in his P.S. paragraphs. The only part I see that could be mistaken for that is his statement that "'not statistically significant' is not the same thing as 'no effect'", but that's trivially obvious to anyone with training in statistics. I read that as a clarification for people without that background.

We'd already discussed PCR specificity ad nauseam, at

https://news.ycombinator.com/item?id=36714034

These test accuracies mattered a lot while trying to forecast the pandemic, but in retrospect one can simply look at the excess mortality, no tests required. So it's odd to still be arguing about that after all the overrun hospitals, morgues, etc.