I don't understand why people are talking about seats here. They couldn't get her through the door. They tried to get her through the door of a plane in Budapest and then they sent her to Prague (which is several hours' drive away) and they couldn't get her on the plane there either.
The husband is suing the airlines because they didn't manage to get her on the plane, even after an hour of trying. For that the suit will not succeed, because the airlines made reasonable accommodation, including delaying the flight for many of their passengers.
And furthermore, she didn't have to fly home to the US in the first place. I live in Hungary, and the healthcare here is not "communist-era", though some of the buildings are. It wasn't an emergency, because she could have accepted treatment in Hungary.