"For the Son of man is come to seek and to save that which was lost...."

Again from A Member's-Eye View of Alcoholics Anonymous:

One of A.A.'s early differences - the idea that alcoholism is a disease - is now no longer unique. While discussion of the exact nature of this disease and its possible cure may well go on forever, no reasonably intelligent person seems any longer to quarrel with this conclusion. However, the impact of the alcoholic's discovery of this fact from the lips of another alcoholic remains undiminished. To alcoholics swamped with guilt and shame, the words "I found I had a disease, and I found a way to arrest it" constitute immediate absolution for many, and for others at least a ray of hope that they might one day earn absolution.

It seems to me that what happens to an alcoholic on his first encounter with A.A. is that he realizes he has been invited to share in the experience of recovery. And the key word in that sentence is the word "share." Whether he responds to it immediately or ever is not at that moment important. What is important is that the invitation has been extended and remains, and that he has been invited to share as an equal and not as a mendicant. No matter what his initial reaction, even the sickest alcoholic is hard put to deny to himself that he has been offered understanding, equality, and an already-proved way out. And he is made to feel that he is, in fact, entitled to all this; indeed, he has already earned it, simply because he is an alcoholic.

In church terms:  change that last phrase to "....simply because he is a sinner" - and I think you've maybe got something.....