I tried that earlier this year for a $1,100 ER bill. The response was, basically, “No, the price is what it is. Bye-bye.”
By the way, since writing the OP, I discovered that unbeknownst to us, the ER also did not accept our insurance. No one told us this. I forget now what led me to believe the charge had been rejected by them due to it being non-emergent. Somebody told me that at some point, but I am not sure who. (Surely no one at the insurance company itself! But then I guess that leaves some unprofessional person at the hospital spitballing and pretending it was fact.)
This did not, in the end, seem to figure into the investigator’s reasoning, but it seems like something else I could have pushed on if necessary.
FWIW that’s what I got the first time I called, as well. But on a second call to billing, for whatever reason, they were then willing to direct me to the department that investigates whether proper procedures have been followed etc. Those are the guys that (eventually) allowed me to make progress on this.