I was reading something about this recently and I think it was over at The Fix. Someone asked this question to one of the doctors where you submit questions. The answer was its not true. The brain actually begins to heal when people stop, but can take up to several years. (Im sure it depends on the severity of addiction and personal chemistry). My guess is this idea got started because people would relapse back quickly before the brain healed. It hasnt been too many years since we have begun to understand how the brain is affected, or how it heals.