How Anonymous Is Alcoholics Anonymous?

Mel Gibson has been sentenced to three years probation including having to attend five sessions of AA for four and a half months and three sessions for the following seven and a half months. Can you imagine Mel Gibson being able to keep his anonymity at an AA meeting? Would the fellow attendees be able to contain themselves from blabbing to all and sundry, "Hey, I go to AA with Mel Gibson. Look, I even got his autograph."?

Something doesn't seem right here. Doesn't sound like too bad a sentence to me though. But I'm not Jewish.