It's not "if the hospital discovers", it's if the patient is uninsured and makes it clear to the billing department that they're hopelessly broke, then the hospital gets flexible with the charges or even writes them off. Many billing departments have flexibility and expect to write off a fair number of bills rather than send them to collections, but they're hardly pushing discounted bills or automatically giving discounts.
If you get lucky you get that. Hospital around where I was (Indiana) rarely did such things. My uncle owed over 250k for emergency heart surgery. That was the discounted price, "as low as they could go".
Dude only made around 30k per year... doing flooring, which could now kill him. Even if he could go back to his work, he had been off work for a couple months. The hospital's "reasonable payments" exceeded his income with work, and was impossible out. More common was a collection agency and eventual court date.
What may work (if he has credit and can cover the lowered amount) is "I can borrow enough to cover the Medicare rate for this and pay it now if that will cover it in full. If that won't cover it then I'm not going to borrow from friends and family when I'll still be paying you and never be able to pay them back."
In his case, that wasn't as likely. Construction work, including flooring, often has slumps and that makes loans more difficult to get. Not to mention the fact that he could buy 2-3 houses for the price of the medical bill (Indiana is cheap) .... and his credit wasn't great even though he didn't carry much debt.
