Earlier quoted context omitted.
Okay, but we're also specifically told to wait for ambulances because they can administer certain forms of care within the vehicle, right?
Like most things, it gets pretty complicated. I went through 200 hours of training (EMT) which essentially helps me sort into what makes me go safe, go fast to a medic en route or a hospital, and go fast to a hospital (where a paramedic can't help much or at all). The goal of all Emergency medical personnel is to get people to definitive care (not EMS). Asking a lay person to know what a BLS (non-EMT fire & police),…
As far as I know, there are also different paradigms for ambulances: "scoop and run" (ie stabilise the patient and take them to a hospital ASAP) vs "stay and play" (try the first line of treatment there before taking the patient to the hospital).
Different countries (with different urban environments, distances, etc.) use different approaches.