It's record is enough that it has attracted millions and millions of members who swear by it as the key to their recovery. And I don't know why anecdotal evidence wouldn't count when annonymity is a key componant of the program. In any event, the millions of sober people who swear by AA is documented and not anecdotal.
How do we know they wouldn't have recovered on their own, or with some other program? We don't. We can't. Any claims of success for AA is pure Blue Sky, with nothing to back it up.