I feel for you. I guess that's the "dark side" of your system. That's something that is hard to understand for somebody like me that doesn't live over there.
Here, if you have good insurance (most don't), you can choose any fancy hospital and you basically will pay peanuts for most procedures (there is always a part you have to pay). Obviously the hospital you choose has to have an agreement with your insurance company or system.
However, if you don't have insurance, you go to a public hospital and get the procedure there. It might take longer, you might die in the waiting room (although pretty rare) but it's free and despite all the complaining (me included) they are pretty competent. Heck, I know of some cases where the private hospitals didn't had the resources to help and sent the patients to the district hospital (which is public).
Not sure if it is true but a couple year's ago I wanted to make some short holidays in NY (I ended going to Malta, long story) but one thing I remember well was the travel agency warning us to take a special insurance because, in her words, "they going to let you die on the street if you don't have one".
I also remember a case that was here all over the news (because, like I said, EU has a health care system in most countries so we can't identify ourselves with your system) about a couple of girls that went for holidays to the states and one of them collapsed somewhere over there and at the hospital they discovered a brain tumor that was promptly removed. She returned to Portugal and a few weeks later she received a shocking $100.000 bill to pay... Not sure how it ended but at the time I was thinking ...? They charge emergency procedures? Lol, I know I must sound silly but I'm so unaware of how things work over there and in the health department things are so different...
Oh, medical care here is completely insane. There's this big damn deal that goes by the colloquial name "Obamacare", a/k/a "The Affordable Care Act"... which still leaves medical coverage in the hands of PRIVATE companies, who charge whatever they feel like, and it is STILL not affordable for those like us, who have no extra money for anything at all, so I don't have it. My husband is a veteran, so he gets his medical care very cheaply thru the VA (veteran's administration) but do they cover dependents? Noooooooooooo!
The reduction in my hospital bill was made possible by a private trust for the care of indigents. The emergency room doctor's bill was also reduced by 95.44%, probably via that same trust. I'm also engaged in wrangling with the anesthesiologists on the same issue, wanting to charge us more than my husband makes in a MONTH, and the surgeon is billing me even more than that! I really don't know where they think I'm supposed to get all these thousands of dollars, but they need to come face to face with a little of the reality that we deal with: WE DON'T HAVE ANY MONEY! We're barely surviving! Haven't heard back from the radiologist or the lab since I wrote them and sent along a copy of the hospital's charity notification, so it's possible they've dismissed my bill, probably via that same private trust.

Andria