Flyitup was actually the closest to how the airlines handle the situation.
First you're supposed to address the passenger with an 'expanded team' (another crewmember, preferably one not directly accused) to ascertain that he's making a serious allegation and that you take such accusations with grave seriousness.
If the passenger persists and does not retract his statement, go and talk to flight operations and the 'duty pilot' to explain the situation to them with as much detail as possible.
They're going to confer with flight operations, a pilot representative and perhaps an on-duty chief pilot and send an operations manager down to the jet to do a face to face assessment and determine if the pilots need to go for futher, more scientific alcohol testing.
If the operation's manager thinks you need further testing, they'll remove you from duty and conduct the tests.
If the operation's manager thinks that the passenger was full of crap and no testing is needed, then all hell can break loose by booting the passenger, etc, and let the passengers know the reason that the flight is delayed, that you're ok, but when passengers make slanderous allegations as such, we've got to adhere to company policy and follow the procedure to the "T".
Instead, if you had angrily addressed the customer, sparking more suspicion that you have been drinking AND rowdy, if you even have a less than perfect landing, it's going to be all over the media faster than you can swipe a credit card on the seatback AirPhone. Or worse yet, even live on the news where Joe Six Pack is talking live to Channel Six aboard a passenger jet with pilots that are rumored to be drunk.
Oh man, imagine the media circus that you'll see on arrival.