Going back to your specific comments. Clearly the universities were not randomly assigned the treatment and control. And the actual number of independent sample sizes is extremely unlikely to give stat sig results at the single percentage digit impact shown. And no matter what they do, for something as complex as mental health, listing out all the confounding factors is hopeless - unlike lung cancer where you are literally sucking tar into your lungs and the sample sizes and effects are huge. Its a useful observational study, but it is ridiculous to call it a proof.
> We know that smoking is linked to cancer through decades of correlational studies and careful analysis of confounding factors, for example.
Yes, it took decades, when there is no proper control set. There are work arounds like backdoor and front door criteria, but yeah - it will take decades of work and looking inside the "black box".
Proofs are for mathematics, not for science. (I share your distaste for science journalism that throws big words like "prove" around without much care, but that's probably not something you can fault the study authors for.)
This is evidence in favour of a theory. It is to be understood within a larger body of evidence. Eventually, hopefully, there is enough evidence in one direction or another that we may draw more or less definitive conclusions.
> I made it a point to not read it, because virtually all social science papers are like these. It's really not worth my time
Nobody is forcing you to read this study, but somehow you seem to assume that your shallow dismissals (to which you are of course entitled privately) are worth anyone's time.