If you want reach a hospital as fast as possible, get in your car and drive.
Paramedics are slower. They’re essential if a problem might be life-threatening or require special handling such as a fracture. They sometimes transport even if their expertise isn’t required, but it’s not guaranteed. If you have a bellyache or high fever, they might tell you to take a cab.
Phoned in the middle of the night, some hotel doctors determine that everyone requires paramedics. With no office job I don't mind wee hour calls, but it's often difficult convincing a hotel that it has an urgent problem.
“You have an elderly man, Mr. Elwood, in 435. He’s confused and can’t get out of bed. He needs paramedics.”
“I’ll send a bellman up right away.”
“No, you have to call the paramedics.”
“I’ll call Security. They’ll send someone to the room.”
“You have to call the paramedics.”
“Maybe you should talk to the manager on duty.”
At any hour, the noisy arrival of the ambulance followed by a train of fire engines disturbs everyone, so persuading a hotel to make the call often takes an effort.