We are a few facts short here.
The over booking/boarding issue is one of them. Are you boarded when you pass the last gate, when you first touch the aircraft, cross its threshold or when your bum hits the seat. An airline might argue its when the aircraft departs with you. Overbooking - the seats available for sale does not equal the number of passengers that can be carried. There are many reasons for this an one of them is carrying crew. Deadheading crew reduce the number of seats available for sale and thus turn a fully booked aircraft into an over booked one.
Deadheading Crew do not pitch up at the gate and demand to fly on a whim. They are told by their Crewing Dept. to go to XYZ and the system has to deal with it.
Regarding who gets select to be offloaded; this is often done by algorithms in a booking system. Those considered to be of a lower commercial value with an airline will be chosen. Very harsh if you are chosen. Deadheading crew have the second highest priority on flights, the highest goes to engineers with tools traveling to fix broken aircraft. They will always be a carried, no matter what argument is put forward.
We don't have a clue what was said by whom and when. We do know this particular passenger has a strange reaction to stress. If this guy is a surgeon I hope he doesn't suffer with episodes such as this with an patient open on the table in front of him.
The customer service game is lost as soon as law enforcement officers show up. The deal with what they see in front of them and act accordingly.
Social media is not always fair. Clips, whilst accurate, may be taken out of context and be lacking the less newsworthy or story undermining build-up. Furthermore, to say a thing is right or wrong does not depend on onlookers shouting and screaming, it depends on the facts. But you can't delete posted social media. It's there forever (United breaks guitars). So even if you are right, your story may not be heard because social media will unfairly shout louder.
What was clear is that UA didn't allow an auction to take place. They relied on their CofC to give them a "legal" right to deny boarding. UA and every other airline might want to review their policies as every now and again a passenger unable to control themselves may be chosen and in return give you a very expensive
PR headache.