It used to be that way here, the reason being, the paramedics can't leave until the hospital takes over care of the patient. However, people were really abusing it, and now, an ambulance no longer moves you t the front of the line. I have seen parents sign something so the paramedics can leave (actually it was a child having a mild allergic reaction). I've also witnessed people arriving in an ambulance and throwing a fuss because they can't skip the line for somethng minor which they likely could have taken a bus to the hospital...or a bad cold they've had for a week that they suddenly felt the need for an ambulance and ER rather then go to their own doctor or a walk-in clinic.
The triage nurse definitely does talk to the paramedic, and then decides whether the patient goes through directly or waits. A head injury might go through right away.
But keep in mind, where I live an ambulance ride is not expensive....might be cheaper then a taxi, I'm not sure. And a lot of people think they don't get billed for it at all, so people here might be a bit more inclined to call for one for non-emergencies.