This "negotiation" you mention works 1. If you know the price up front 2. have the leverage to negotiate.
And guess what, you have neither of them. This law changes one of those, so that shopping around is at least possible.
Aside: I'm surprised a lawyer didn't sue a hospital over Informed Consent via no billing knowledge.
In emergency situations this is hard to do, but I've done it numerous times when needing non-emergency health care. I even call around asking about prices and the cash discount. Oddly enough, a co-worker and I both had the same procedure (back issues ugh) last year at the same doctor. He used his insurance, and I asked about and went the cash route. I ended up paying less for the exact same thing because of how his deductibles worked.
It was the end of the year and I guessed I would not hit my yearly deductible so paying cash was the right move.
When I had knee surgery years ago, and had good insurance at the time, I asked the doctor about the price just to see. He was quick to say if I wanted/needed to pay cash he could work something out.
So they are out there, but you might have to do some digging.
And again, emergency situations are a completely different beast.
If you don't know the bill, they can't tell you the bill, and they have no way to get the bill until weeks later, how can they "negotiate" when nobody knows?
Frankly, that claim sounds like a pile of you-know-what. My bet is they take your money, and then bill you for the rest.