While Gelman does point out to issues that may invalidate this paper (test specificity, mostly, and noisy weights, potentially) there does not seem to be any "cherry picking" involved.
I would say even if the study is merely statistical error, using it to give an implausibly low estimate of the IFR that just happens to fit the agenda of one author qualifies as cherry picking. A priori you can not use a test with high false positive rate to do a study like this unless the prevalence is much higher than the false positive rate.
