United owned the plane, their aircrew wanted the person removed.
Once the cops are called it's not the role of them to mediate or judge if United was right for having him removed. That is a contract dispute and a matter for civil court. It is their job to remove the person from the plane that the aircrew want removed.
So the cops have to escalate if the person refuses to comply. It's the job. You can't just say "well, he says he won't cooperate so I guess we just ignore the law this time". It's part of the powers society entrusts government with to enforce laws to use force when necessary, and unless your an anarchist libertarian type it's part of the social contract you support if you want a government of laws.
They can't go in and ask him to leave and then say "oh, he says no, so we are just going to leave". There are calls like this where you don't get to exercise discretion. If the law says a person must leave an airplane when the aircrew requests it if the aircrew calls the police the police have to enforce that. There may be, and in this case was, a deeper problem of contract dispute and mismanagement involved bur mediating that or judging that is not the role of the cops on the ground there.
As I have said before, the actions of everyone involved put the cops in a no-win situation. The best possible outcome once they were called would be the doctor voluntarily going off the plane with them and then filing a civil suit against the airline. If they came in and the doctor refused to go with them and they told United "oh well, we asked and he refused" they would not be enforcing the law and not doing their job. Removing him with him resisting was a no-win.
United caused a mess and then put the officers in a no-win situation to clean that mess up. It's the same crap you see in schools where teachers will call cops for something like a child refusing to put away a phone and put officers in a no-win situation. There are situations where people never should be calling cops in the first place but they do, and once they do the cops have to do what the law says.
This is similar to an eviction I once worked. The eviction papers were properly done and issued by the court, but the person refused to leave insisting that the eviction was improper because the landlord had defrauded her. However as a deputy I had properly issued and legal eviction papers so her deeper dispute with the landlord couldn't play into the decision, we had to remove he from the premises and because she refused we ended up having physically remove her and when she went back in had to charge her with trespassing. She did pursue legal action against the landlord in civil court and I have no idea how it ended with that- but her underlying civil case wasn't a factor we could consider.