I really think it depends on the person and their individual will power and the reason why they've decided to deal with their problem in the first place.
I have a friend who is an alcoholic; he didn't attend meetings or rehab. He threw himself into his work and so far three years later he's doing ok.
He told me he woke up one morning outside his front door. He decided then and there to stop drinking.
Personally I think AA or rehab are good support mechanisms and that is very important when a person quits drinking. I would encourage anyone who suffers from addictions to seek help within a secure set up or group. Stopping is one thing; not starting is another. I also think finding the root of the problem for some people is equally as important as stopping.
When we face difficult times in our lives we need all the support we can get.