I absolutely agree with your philosophy. In my ambulance days I had a 'chest pains' patient who was ambulatory when we arrived. He refused a gurney, but agreed to take a ride to the ER with us, so the attendant got in back and the guy rode in the passenger seat, complaining about having to do to the hospital the whole way.
At the hospital, we persuaded him to get in a wheel chair, took him to an examining room, he insisted on getting on the examining table himself, got out of the chair, and went nose down. Resuscitation attempts failed. That was forty years back. These days, our local paramedics do c-spine precautions on anyone who could even remotely possibly have sustained damage. They take a similar approach with cardiac patients.
A few years ago, a friend and I were walking home from a bar when we happened upon a guy lying in the street. He'd been clipped in the face by the outside mirror of a passing Jeep and knocked to the ground. He was incoherent, listless, and it didn't look like his pupils were responding. There were no no obvious wounds and there was no blood on the pavement.
When we walked by, his friends were standing over him, starting to grab him by the arms as if to drag him, saying "we need to get him out of the street." Michael (my friend) was a WSI lifeguard, and I had no formal training aside from basic first aid and CPR/artificial respiration, but I knew enough not to move someone with a likely head or spine injury. We both said "NO!" in near-perfect unison.
We rounded up a few fellow inebriates to stand around and be visible so no one low to the ground would get run over. Within a few minutes, EMS arrived, and we told him what we'd seen. And then we left, because we'd done everything useful we could, and we stayed we'd just be in the way with all the other gawkers. I never learned how that turned out.
I don't know what it is about this thread, but something's got my anecdote machine going.