Let's pick this apart:
> This is true, but it's true for almost every observational study, and IMO too easy a dismission.
It's also a correct dismissal. The vast majority of results don't replicate. It's super-easy to come up with results like this paper just by playing around with what you control for (with a 5% of a false positive each time) until you get the result you want. It's almost impossible to tell if this happened. There are many similar issues.
> You can use this reasoning to dismiss, or more likely, to cherry-pick probably 95% of all scientific results from economic/medical/social/nutricion/climate science.
And you should! You should believe results only once they've been replicated multiple times, by multiple communities, with multiple methodologies.
> I'd say the onus on sceptics in this case
The onus is on the people presenting the result, in all cases. That's the scientific process. The authors need to defend the null hypothesis as vigorously as you can.
> This paper is likely headed for a serious economic journal, where it typically goes through at least days of labor to scrutinise the execution/details/methodology in peer review. I'm not invested enough to volunteer for that.
Have you ever gone through a peer review process? Seriously?
I understand you're not invested enough to do that, but neither are the reviewers. It's a volunteer position with no credit or upside. Most give a cursory skim, and either accept or reject. It's no better than chance.
Seriously. NIPS did a study, and found it is literally no better than chance.
Of my own papers, I've only had one where peer reviewers did an in-depth read. For the rest, acceptance was completely random. Reviewer comments often have little relation to the actual paper (many reviewers just skim the abstract and the intro, and don't even fully read those).