Hi,
No sir---they cannot---the UNITED cannot once the person has boarded and claimed their seat---.
The person has not committed a crime---he does not need to follow any illegal orders---.
As he has not committed a crime---he cannot be ordered either---.
That compensation is pre-boarding---. Once boarded---the possession of the seat is 9/10 in the favor of the ticket holder---. The airline can only request---.
This particular case, there are 2 separate problem.
1.) Can the pilot ask you to leave their aircraft?
2.) Can Authority remove you from an aircraft?
For Question number 1.
Well, United can reject you from their premises given they did not discriminate you on behalf of age, race, gender and religion.
A plane is like a restaurant or a club, which have a fire safety related serving capacity, and when it is at capacity, in case of an airline, they can either refuse people service or reject people already in their premises, again, given if the rejection is not based on race, gender, age or religion. There are no law to criminalize action regarding acceptance of service and refusal of service, so in term of law, the pilot, acting as an agent of the airline, can ask to anyone to remove themselves from their plane, much like a night club can ask you to leave their premises when they are over capacity.
Since there are no law to regulate this, the "RIGHT OF SERVICE" is lies within the power of the customer, however, the equally strong "THE RIGHT TO REFUSE SERVICE" is lies within the Owner of the premises.
Simply saying, given if they did compensate you, and did not break the existence law, the pilot can actually ask you to leave the aircraft, it may not be your fault, it can be the airline fault, however, since there Right of Service and Right to refuse Service is equal in dimension, it's basically up to the airline to take your business.
For question 2.
Regardless of the pilot action, a federal law called 49 U.S. Code § 46504 - Interference with flight crew members and attendants exists.
Since it is not an criminal act for a Pilot to ask you to leave, you refused to follow the pilot's, which is a part of the flight crew, instruction, that person, at that point is breaking the 49 U.S. Code § 46504. And UA can call authority to forcibly remove you from the plane.
As per this particular case,
It is not Dao fault when he was asked to leave, as you said, he did not say or do anything illegal, however, United did not break any law for asking him to leave, United, would have break the law if they are the one who physically remove Dao from the plane, but facts remain, this is not the case.
And when he was asked to leave and he did not comply, Dao, at that point, is breaking the law 49 U.S. Code § 46504. United then have the right to ask for authority to remove him.
This case will be very much different if the officer in question did not use heavy handed tactics to remove him.