I can see where everyone is coming from on this in feeling like this term is a cop out or an oxymoron. I think it really refers to a stage of alcoholism that alcoholics may or may not experience.
The very existence of this term was actually a lightbulb turning on for me. It's true that the stereotype exists of people who are staggering around, raving drunk all the time. When you recognize that someone can hold down a high-status job, keep a driver's license and sustain relationships with family members --in essence, function the way non-alcoholics do -- AND still be an alcoholic, you're breaking the wino-under-the-bridge stereotype.
That's not to say that someone can't transition from a "functional alcoholic" into someone whose job or relationships start to suffer, or whose relationships have always suffered without an obvious cause. I still find myself asking whether my dad's really an alcoholic because some days, he can have just one drink. That doesn't sound like an alcoholic to most people because they don't see him earlier that day when he's shaking from withdrawals, or on the days he throws back a whole magnum bottle of wine.