Not sure if it's still the case, but in 2011, the Charlotte Airport Police were responsible for medical response inside the terminal and for an aircraft attached to the jetway. Middle of the summer time and I had a passenger (male, mid 70s) apparently run from the other side of the airport to catch our flight. He's totally out of breath when he gets on board (we were parked at a remote spot with no jetway out at the end of the E gates) and sweating. He gets about halfway to his seat and collapses. My FO sees it happen, grabs the radio and calls ops to request medics (which is company policy). Meanwhile out FAs go to work on the guy.
And then we wait.
And wait.
And wait some more.
My FO and I call ops and ramp control 5 or 6 times over the next 10 minutes while we wait for the medics. Meanwhile the guy in the back is still breathing... kind of... but unconscious.
12 minutes after the FO called, two cops walk over to the airplane and yell up the stairs to ask if "somebody needed something". They don't even have their med bag with them... it's back on their golf cart they left parked inside the terminal. One of them kind of ambles back inside to get it while the other one comes on board and starts working the patient.
After that I never bothered calling ops for medical and just called ground and asked them to roll the trucks to the gate.