We have private emergency rooms. We call them urgent care and you can go and see a qualified physician with allied health services (radiology, pathology). If they can fix you up they will. If not you get transferred via ambulance to the nearest public hospital and triaged as required.

I took my kid to one last weekend as they had been diagnosed by our family Dr as having pneumonia. The emergency physician ordered chest x-ray and full suite of pathology and we had results in less time than we would have waited in the public hospital waiting room. Yes we paid.