Liz -
It takes about two years of sobriety for the body to make a recovery. That is because the addiction has basically ravaged every part of the addicts body.
So even though the person may be sincere and "genuine" only time will tell how long sobriety will last. Some things that make it more likely include a support group, regular visits to a doctor (make sure it's a specialist), the best nutrition, exercise, and avoidance of triggers.
Some people don't like AA because of the religious overtones and the "culty" feel that it produces. It's not for everyone. However, there are other alternative out there. There are support groups now being offered that have no religious affiliation and do not have the same culture as AA. Many people find them more appealing.
With a little research the right fit can be found.
Best of everything!