It probably depends on the hospital/clinic. Where I was, they asked for payment when I left. They didn't ask for evidence of my ability to pay when I arrived, about to collapse and puking on their floor. They treated me first (for a full day), then asked for payment. Contrast that with a trip to the ER I had in the US, where I had just been stabilized after anaphylaxis from an allergic reaction. While I was still being wheeled back, they were asking how I was going to be paying for that, if I had insurance, etc., trying to determine my ability to pay (presumably so they could determine what level of care to give me).
I would probably put both "individual pay" and "fully socialized" above our current system, or maybe a mixture, but one where there's true competition instead of the mess we have now.