Actually that can't be farther from the truth. Addicts can't rely on themselves to get off of drugs because they got themselves hooked in the first place. They need to get their power from somewhere else, be it God, Jesus, nature, a tree, the Force, or anything is the only way.
Most addicts learn that it's not drugs that are the problem. Personally, I don't have a drinking problem, I have a living problem. The drinking is only a symptom. I need to learn how to live a good, honest life that is free of resentments, dishonesty or anything else that is going to keep me from feeling guilt, shame, remorse or regret. And the only way to do that is to give my life up to a Higher Power and understand that I can't change anything that happens in my life. Knowing this will keep me from going back to drinking. I don't feel it is God's will for me to drink again. Anyone that uses that as an excuse doesn't really have a grasp on their Higher Power.