This is actually untrue. The way they get to the hospital has nothing do with it, everyone is given a score upon arrival according to their symptoms, and are seen accordingly. Someone who was driven in with asthma symptoms would be seen long before someone brought in by ambulance with a broken leg. It sometimes appears that people who are brought in by ambulance see dr's quickly but in reality, they wait just as long as people in the waiting room, they just wait more comfortably.
As stated, my comment was from what I have been told directly and from what my DH saw while working in a hospital. While you may have been told (and observed) differently, and while it's certainly possible that the policy is as you say, my views are based on what I have been told (including by Drs working in hospitals).

No one should be taking this to extremes (eg: someone with a papercut in an ambulance is hardly going to be seen faster than someone with chest pains who has brought themself in) but that is what I have been told in no uncertain terms.