While one (especially United) might expect this to make no difference, the letter of the law is what should have been followed in this case.
Police often tend to make up nonexistent laws as they go. Those imiganiry laws might even sometimes make sense. But "with great power comes great responsibility" and that responsibility is to only uphold the laws on the books.
In the case of the United passenger, he was disturbing nobody until after they tried to force him to leave.
He doesn't have the right to because the airline wanted them off in breach of the contract of sale and the guy said "yeah no".
Refusing peacefully to go along with the fiction the airline has created isn't causing a disturbance. You can't force someone in to a "disturbance" state if they're just sitting there。
That said, the captain's decision does not make him immune to lawsuits, disciplinary action, etc. but on his plane, especially while flying, temporarily he IS god.
If you want to sue afterwards you are allowed in America to do so. But the captain should be allowed to call police in to remove anybody. Period.
I bet if they knocked her unconscious and dragged her from the pool, they'd be in trouble too. At least I hope so.
Isn't the whole point of police training to learn to deal with these situations safely and as peacefully as possible? If you can just shoot or punch everyone who's causing a disturbance, what do you need any training for?