I find most of this post persuasive, but it seems to me like there shouldn't be excessive certainty on either the yes or no column here. The author's claim is not "no, this is false" but "the study is not bad, for what it is, but is highly limited in the conclusions that can be drawn from it, and it has some serious limitations." It seems reasonable to remain agnostic for now and pursue further studies on the topic that attempt to more accurately correct for other confounding variables.
This also gives me pause: "It is certainly possible that some pesticide is causing adverse health effects at the currently used levels (although there is no current evidence for this)."
That claim seems to me to be false if we include studies on occupational use of pesticides [1]. It could definitely be the case that the residues that ordinary consumers encounter are entirely non-toxic, but again, it seems to me like the jury is still out on that.
[1] https://journals.plos.org/plosone/article?id=10.1371/journal...