Basically, there were two grounds upon which United might have legally denied a flight to the doctor: their own contract rules 21 and 25. First, about Rule 25: it specifies circumstances upon which United may deny BOARDING when they've oversold the plane. The doctor, however, was already boarded so Rule 25 can not legally apply. So, we're left with Rule 21, which covers circumstances under which United can deny transport. Now, United says the passenger was belligerent to the crew, which WOULD be a proper reason for denying the doctor, EXCEPT that what they were asking him to do was an UNLAWFUL request. He had already boarded, he was under no violation until he was ordered to get off the plane UNLAWFULLY. For example, if United had asked the doctor to dance on his head he was entirely within his rights to become hostile to that order. United will pay. United will pay big.