The long argument highlights the absurdity of rigid no-transfer rules. (Technically, children under 18 don't need to show ID. The airline would not be able to prove it was the wrong child in the seat if the family doesn't disclose that information.) Eventually, the family says, for the sake of taking off, they'll put their son on a lap. "It's come too far," the family is told. "At this point, you guys are on your own."
They get removed from the flight at midnight with two small children and, according to the family, wind up spending $2,000 to book a new flight home.
In the wake of David Dao being dragged off a United flight, this is a bad look for Delta even if they had some ground to stand on through ticket transfer rules. While many airline inconveniences are the result of customers looking to fly as cheap as possible, forcing airlines to cut amenities, there's little sympathy out there for airlines when they overbook a flight.