I've been told, "Don't worry about the copay," after telling them I could not afford the $400 copay, and I got up to walk out.
Somehow they thought $400 wasn't a big deal a month later. I couldn't afford $400. It wasn't like "I can't afford $400 today, but hey, no problems on Tuesday."
Yeah, just because they will treat you without medical coverage does not mean they won't bill you for it too. And then you're job is to prove -- by coming up with copies of all your bills for the last 18 months, plus proof of income for 18 months to (and making all those copies cost time and money too) -- so they can decide for you how much you could afford.
Do you really think they don't bill people, simply because they don't have insurance?