The Cochrane meta-analysis has arrived at opposite results to that debunking, based on 21 recent randomized studies. It's interesting how many comments in this thread are pointing to the older results as if they debunk the newer ones.

Maybe AA doesn't have to be very effective for it to be more effective than psychotherapy?

That information is, at best, out of date. The new Cochrane study links to a number of studies which show a far higher rate of abstinence than 5% for subjects randomly assigned to undergo treatment which encourages them to be part of the AA fellowship. It reports a 41.8% success rate — actually abstinence from alcohol rate — 12 months after treatment.

That's a fine success rate for any addiction for any treatment.

You can go down multiple paths multiple times before things start to stick. You also have harm minimisation to think about.

How many celebs who go to 'rehab' with the best money can buy then relapse? You don't just write off their rehab, you get them to go again or they might try something different.