MarkerInbound, why did you shake your head? Looks to me that the controller did exactly what they have to do, not give priority until an emergency is officially declared. It sifts out those that really need it from those that have got themselves into a "tight spot".......
Because the purpose of the radio to communicate. The inbound flight told ATC they have a person aboard who needs transport to a hospital. Both parties being native English speakers, I'm sure ATC understood the situation. Yet he wouldn't do anything until the magic code words were spoken.
And the FAA AIM says:
6-3-1 Distress and Urgency Communications
a. A person who encounters a distress or urgency condition can obtain assistance simply by contacting the air traffic facility or other agency in whose area of responsibility the aircraft is operating, stating the nature of the difficulty, pilot's intentions and assistance desired. Distress and urgency communications procedures are prescribed by the International Civil Aviation Organization (ICAO), however, and have decided advantages over the informal procedures described above.