The Dr became a person no longer allowed to be on someone else's property and it is the job of a police force to remove a person that is no longer welcome one someone else's property.
It is not the job of police to resolve civil disputes or enforce artificial qualifications to said disputes after a deal has been made through contract. So, for example, if you are at a tag sale on someone's lawn and they sell you a lamp for $10, you get a receipt, and the lamp, they cannot then sell it to their neighbor for $40 and promise to give you $20 compensation, calling the police to violently enforce their involuntary changing of contract terms. Their telling you to get off their property and taking the lamp and receipt is theft unless they have your voluntary, un-coerced agreement to renegotiation/re-bartering.
In the case of an airline seat, you have rented that property (the seat) to be transported to said destination. Their taking of the seat is theft just like in the example above. If you were renting an apartment and the landlord kicked you out after you had paid rent for the month, saying he got a better offer from someone else, he still cannot throw you out in the cold. You rented his property through contractual agreement and did nothing to violate that contract.