I can beat that.
We were boarded (AA) but had to wait for over an hour for them to clean up a fuel spill on the tarmac, caused by a faulty shut-off valve.
Of course, we arrived in DFW nearly 1 1/2 hours late, ran through the airport, only to have them shut the jetway door in our faces. Well, that's an exaggeration - we were standing at the counter.
Next flight was in 4 hours.
They are a foul collection of humans.
In defense of AA (go ahead, throw virtual tomatoes...), I have an equally astounding story... but just the opposite of your experience.
Summer 2007 my son and I were going to fly to Rome... LAX-ORD-FCO. Our flight was to leave LAX at 9am and arrive ORD so we'd have a three hour layover before the flight to Rome departed. I thought it was the perfect schedule... a few hours in O'Hare to grab some lunch, and gave us plenty of time in case something went sideways.
Or so I thought. Check in early at LAX and wait. And then we're told that due to thunderstorms in the midwest, the planes are behind schedule... so the planes that were supposed to depart LAX in the morning were still on their way.
We waited a while and after an hour we were finally given a new departure time: exactly three hours later than scheduled. Which means my layover had just been reduced to exactly zero. I asked the CSR at the gate what would happen, she punched some stuff in the computer and told me "well, there are 19 of you on this flight that are making that connection. They'll hold the plane for you."
We depart LAX and have an uneventful flight to Chicago. As we are preparing to land, the FA announces that she needs everyone to stay seated when we land, the 19 connecting to FCO are to get out first. They parked our arriving plane at a gate adjacent to our departing plane. Everyone cooperated, we walked (ran...) off the one plane and onto the next. They closed the door and we pushed back from the gate.
As we're in the air, I thought "whew, that was close... but we made it." Followed by my next thought: "what about our luggage?!?"
Got to Rome, luggage was there too. The baggage handlers must have been moving faster than we did.
Does go to show that the airlines are capable, when they want to, of allowing people to make their connections.