Thanks for the heads up.
Yes, after listening, the study seems to be very flawed indeed. It's the case of most studies like that... it makes for click-baity articles, but statistics are a bitch. Not only in social sciences, but also in very technical fields, few people actually know how to properly account for confounding variables, use statistically significant samples, etc
Overall, for my own health decisions, I only trust meta-studies. And often, it turns out that the effects are of the order of a few percent at most. So best you can really do is just live an active life and not eating crap.