I find it interesting that the DSM-V does not use the terms alcoholic or alcoholism. If you go to counseling (in most places in the U.S., anyway) for alcohol-related problems, the paperwork will likely not state you are an "alcoholic." The terms are "alcohol abuse" or "alcohol dependence," and the diagnostic criteria tend to focus on behavior and cognitive processes rather than a "medical" definition. Maybe that's because regardless of genetic factors, the "cure" (if you can call it that) requires changes in behavior and thinking.
I think I was genetically predisposed to addiction, and environment played a huge role, but my alcohol dependence is entirely the result of my own choices.