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But I'm just talking about the statistics here, and specifically that saying "correlation is not causation" is a bit overused. Researchers know about it too, those four words don't magically dismiss all statistical studies. Most modern statistical approaches are explicitly built to try and help address these sorts of concerns.
There could well be other flaws with their statistics, and even if there is causation they could be failing at theoretically motivating or connecting it to their overall narrative. But it takes more than four words to make that case.
EDIT - just acknowledging that you've since edited your comment to add concerns about p-hacking and reproducibility. And that may be the case - but it wasn't what I was responding to in my initial comment.