Okay, but we're also specifically told to wait for ambulances because they can administer certain forms of care within the vehicle, right?

It kind of depends. EMTs are able to do some things, paramedics are able to do more things, and the hospital itself can do even more things.

I live about 6 minutes from the closest ER. If an ambulance can get to me in, say, 3 minutes, it's still not clear if it's better for me to get myself to the ER on my own. Maybe I get an ambulance with EMTs who aren't trained/authorized to do what needs to be done for me. Maybe I really need to be at the hospital within 8 minutes or I'm going to die, and waiting for an ambulance just isn't going to cut it.

But I think, statistically, people should usually prefer to wait for the ambulance. It's just that specific circumstances can make that the wrong move, but most people won't know when that's the case.

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), EMT (Ambulance), Parmedic, or MSO can take care of, or even what the differences are, is, I don't think, super useful. The red vehicle shows up and takes you to care.

In the case of MCI, EMTs can a) give aspirin or nitro (rx), b) have an AED and lots of CPR training but have to stop the vehicle to give effective compressions, c) a radio and the ability to meet up with Paramedics.

Paramedics have more complex treatments (drugs) and EKGs, but it's still 2 folks in a truck, not a hospital. They can do amazing things.

But as the joke goes, sometimes the best treatment is High Volume Diesel Therapy (burn rubber).