I doubt the guy has much of a legal case. Once the Airline asks you to leave and you dont, you are trespassing. The police used force, mostly because that's what they do, but also because he was breaking the law. Overall, it's horrible customer service by United and a childish display by a grown man.
On this situation, they might have a case as the Dr bought a seat, was allowed to board and take his seat and was not in combative in anyway prior to the Police showing up.
This was an operations issue with United with 4 of their employees that they didn't want to rent ONE CAR for a 4.5 hour drive to Louisville.
United did not overbooked or oversell this flight. UA's Operations Division decided to take seats from paying get passengers who already boarded and give those to 4 employees instead.
Police should not have been called in this situation as UA could have easily handled this situation by upping up last financial offer for final seat and or "pay" an employee or two to drive to Louisville instead.
All of those options are cheaper by 1,000 times or more of the bad publicity and future litigation (which UA will settle out of court).