I 100% agree with the study cited in your post Nicam.
Getting back to your specific question...chicken/egg. I spent the best part of 20 years drinking. I always had some degree of anxiety as far back as I can remember and once I discovered rum and coke at University, my anxiety dissipated. Hmmmmm.
Having spent a few years in AA, I would be hard pressed to think of anyone who did not drink because of depression and or anxiety. Perhaps the "chicken" end of things. Then there was the contingent of bi polar and some with diagnosed PD's. Let's face it, no emotionally healthy individuals abuse alcohol.
Once I decided to place my low ball glasses on the top shelf, I sought therapy and was prescribed anti depressants. Anxiety dissipated. Too bad I didn't go that route before I medicated with alcohol.