Independent researcher and journalist Maia Szalavitz, co-author of Recovery Options (reviewed here), takes on these critics. It's worth reading. She writes, among other points:
"Contrary to the Journal’s claims that AA “hasn't been subjected to the gold standard of medical experiments, the double-blind randomized clinical trial,” there have been several trials that did just that.
They just didn’t happen to find an advantage for AA ...""[As] one of the studies covered in the Cochrane review found, if AA has any advantage over other treatments that do not carry its baggage of involving surrender to a higher power and asking his help with 'character defects,' they haven’t yet been found in years of study."
Maia's comment is in STATS.org, website of the Statistical Assessment Service. Source.