Well, talking from personal experience, this is how the conceived "no care" attitude evolved.
On one occassion, an inbound requested medical assistance for a sick passenger. This message was relayed from approach to the tower, who then contacted the fireservice.
The fireservice then alerted their own paramedic team who contacted the local ambulance service for assistance.
Meanwhile, the inbound crew had contacted their handling agent, who thoughtfully dialled 999 for the emergency services to attend...they told no-one of this action.
Airport Ops were notified, who also contacted the airport fire service.
Unknown to airport Ops, ATC had liased with the fire service paramedics for the aircraft to be met on a runway exit, as the aircraft had airstairs.
Whilst the Ops manager sat at the arrival gate waiting on the arrival,he became anxious that their was no medical presence.
He therefore radioed the fire service to confirm they were on their way to the stand.
The fire service replied "negative, we're already attending a medical emergency."
He instructed the fire service to call for an ambulance, which they did.
Long after the one and only medical emergency had been dealt with by the airport paramedics, 3 outside ambulances arrived.
Understandably, the local area health authority wanted financial recompense for the unecessary call-outs.
Once the dust had settled, blame for the fiasco was quickly put down to the fact that there was no clear line of action.
Therefore, the responsibilities were clarified, and I am pretty sure most UK airfields now adopt a similar procedure, that being:
After a request for medical assistance, ATC notify the airport fireservice (or airport paramedics if it is a distinct operation). If known, the handling agent should also be notified. All further action of a non-ATC matter becomes the responsibility of the Medical services, the Airport Operator and the Handling Agent.
RawData, of course as an ATCO, I would go out of my way to help, but please, don't expect us to do things which are the published as the responsibility of others; my initial reaction was to PennineBoy's question as to what would have happened had the aircraft been an aircraft accident as opposed to one requesting medical assistance.....totally different situations, a grossly unfair comparison, and a disgusting slant at the guys and girls who do their best to provide what is, in my humble opinion, a damn good service for you all.