As others have pointed out, United's Contract of Carriage does not permit United to demand that a passenger deboard an oversold plane to make way for another passenger. United was limited to preventing the passenger from boarding the plane. Once the passenger took his seat on the plane, it was his, and the only circumstances that could justify United removing him from the plane are those in Rule 21 of the United Contract of Carriage, which provides that "UA shall have the right to refuse to transport or shall have the right to remove from the aircraft at any point, any Passenger for the following reasons . . .," none of which concerns oversold flights.
Further, Rule 21, and its use of the phrase "UA . . . shall have the right to remove from the aircraft at any point, any Passenger," removes all doubt that Rule 25's reference to "denied boarding" does not encompass removing passengers from a plane that are sitting in their seats.