Does not matter because they were there at the request of United Airlines.
If you think about it, it was a robbery of the Doctor.
He paid for the seat and should have more than a reasonable expectation of arriving at his destination. I would have resisted as well. Don't take that the wrong way, I am all for law enforcement.
If someone came up to your car when you are driving and demanded that give it to them would you hand them the keys?
I know I would not.
Yes, security WAS there at the request of the airline, but I highly doubt that the outcome that manifested was the outcome expected. Suppose you had a neighbor that was playing his music a little too loud, a little too late at night, so you call the police. And the police showed up, kicked the neighbors door in, and just shot the stereo and the neighbor. Is the death of your neighbor your fault because you called the police on him? Of course not. Extreme analogy, I know. And, it only covers part of the situation; the calling of security. My guess is that the expected outcome was that the doctor would simply get off the plane when security asked him to.
I wouldn't equate this to robbery of the doctor, because he still would have been flown to his destination. He would have arrived late, but he would have been compensated for the inconvenience. This a not the same thing as a car jacking. In a carjacking, my car would be taken from me, with no value given to me in return. This would be closer to imminent domain, than a robbery. (Though, that's an imprecise comparison, too)
I'm not defending UA. They made bad decisions. What I am doing is stating my personal opinion (which is meaningless, in a legal sense) that EVERYONE was wrong, to some degree.
If UA really needed to clear some space for employees on that flight, it should have been done prior to boarding. The security force could probably benefit from training on how to interact with the general public; I'm also guessing that there may have been some miscommunication due to the accent of the doctor.
And, the doctor... I expect a doctor to handle disappointment in a more mature manner. I understand that he had somewhere important to be. Apparently, so did everyone else on board. He drew the short straw. It's not fair. But, a doctor, of all people, should have a very deep understanding of the unfairness of life. Frankly, after that performance, I would never be a patient of that doctor. And, if I were, I would find a new doctor, after that video went viral. A little calm reasoning, on his part, may well have kept him on board, injury free. Had he calmly explained to the stewardess that he understood the dilemma that faced the airline, but he was expected at a hospital for a serious medical situation, and here, would you please call this number, or have the pilot call, to verify.... The situation may never have gotten out of hand. Or, maybe he still would have been asked to depart the aircraft. I don't know; no one knows, and now it's impossible to find out.
It's all a moot point, to me. I refuse to put up with airports, so it's doubtful that I will ever find myself in an aircraft, again, anyway. At least, not on a commercial airliner.
I guess my point is, before we all crucify UA, let's consider how all parties involved could have handled things differently, and consider the points of view of everyone.