United Contract of Service
Under Rule 25—on page 35 if you print it out—the agreement says exactly what happens if the flight is oversold. “If there are not enough volunteers, other Passengers may be denied boarding involuntarily,” the language reads. (Of course, the deplaned man was not denied boarding, he was already boarded.)
The language continues however, shining light on how these “other Passengers” are chosen. It’s not random, it’s “in accordance with UA’s boarding priority.” That means that if you have a higher fare class, have a complex itinerary, have status (e.g. gold or platinum), have checked in early, or are a frequent flier, you are less likely to be asked to take the next flight. Even if it’s just a frequent flier card that you never use, it might save you from being forcibly dragged off a plane.
Any kind of priority is better than no priority, when it comes to not getting forcibly removed from a plane.
For passengers looking to take advantage of the budget seats offered, this unspoken ranking and largely unknown class system is important to know. Though companies take great pains to say otherwise, if you paid less, you are not as valued a customer.