I saw this in the fantastic documentary series called The Sixties, which is on Netflix. They show a lot of great footage from the killing. This comes from episode 3, which centers completely on Kennedy's assassination.
Prior to the 60's, there was no real coherent/modern emergency medical services occurring in the USA. Training was not standardized and you may have just gotten 1 guy driving a modified hearse, an actual crew of medically trained people, or nothing at all. It was common that funeral home hearses were the primary transport to the hospital. They provided basic if any first aid. The hearse was vehicle of choice because they were one of the few vehicles around with enough available space in the back to accommodate a supine body. Plus, given the fatality rate of motor vehicle accidents, (49,000 motor vehicle crashes resulting in death or about 24.9 per 100,000 people in 1965) they could also take care of the body if the patient was DOA.
The EMS White paper was published in 1966 by the National Academy of Sciences as the paper "Accidental Death and Disability: The Neglected Disease of Modern Society." The study kick started modern emergency medical services as we know them today because it correctly identified that lots of people were dying fairly needlessly. The paper put forth changes to the system in order to reduce overall morbidity and mortality from accidents.
"The EMS White Paper states that in 1965 there were 52,000,000 accidental injuries. Of these accidental injuries there were 107,000 killed, 10,000,000+ disabled and 400,000 permanently impaired. The estimated costs were $18 billion (this is $117 billion in 2008 dollars)."
The EMT White Paper identified (among lots of other things) there was no fixed definition of an ambulance. In 1966 the National Highway Traffic and Safety Administration set standards for ambulance construction. The specification for ambulance design laid out these points and is referred to as the triple K specification.
Temperature
The ambulance needs to be able to operate if the exterior temperature is between 0 to 95 F
The interior minimum temperature needs to be maintained at least at 50 F
Speed
The ambulance must be able to maintain a sustained speed of 65 mph
The ambulance must be able to pass at 70 mph
Acceleration from 0 to 55 in 25 seconds
Hills
The ambulance must be able to travel up a 3 % hill at 55 mph
In additional the ambulance must be able to travel up a 35% hill (steep) at 5 mph
Fuel
Range of 250 miles w/o refueling
Water Crossing (fording)
The ambulance must be able to make 3 passes through 8 inches of standing water without flooding at 5 mph for a distance of100 feet
Width less than 96 inches excluding mirrors
Loading height no more than 34 inches
Must undergo a static pull test
2200 lbs static load test in all directions, front, back and verticle
No dynamic load tests
No crash test dummies
As EMS progressed in the USA, so did ambulance design. To be able to meet the rigor of triple K standards (2008 specs) as well as the advances in pre-hospital medicine and safety, ambulances have had to evolve into what we see today.