In my experience, as both an interviewer and an interviewee, interviewers are just trying to find a reason that you do not fit the mold. Because how much can you learn about a person in 1 hour, really? So if there are any glaring red flags, like a DUI, you get rid of them and move on to the thousands of other candidates who don't have that in their background.
The same would be true if you said "I had to leave my old job because it was interfering with seeing my parole officer." They don't really care if you have a drinking problem or not, it's just a red flag they don't need to deal with.