Why does AA hang together?

I've heard it said that the reason we have fellowship is because we're only ever one drink away from a drunk. The crisis that brought us together never leaves us, which is why we're hanging together.

The book Alcoholics Anonymous offers a different view:

"Unlike the feelings of the ship’s passengers, however, our joy in escape from disaster does not subside as we go our individual ways. The feeling of having shared in a common peril is one element in the powerful cement which binds us. But that in itself would never have held us together as we are now joined.
The tremendous fact for every one of us is that we have discovered a common solution. We have a way out on which we can absolutely agree, and upon which we can join in brotherly and harmonious action. This is the great news this book carries to those who suffer from alcoholism."
This reflects my experience: the bond of a common solution is even stronger than the bond of a common problem.