That's 100% the hospitals fault, no other profession would get away with not knowing how much the service they provided you costs and then making up a number to charge you.
how come the US is so opaque about pricing? Any other country i have been to (national insurance or not) has been absolutely transparent about pricing of healthcare. Including a GP in a tiny village in france who didn't speak english who sew back the skin on a finger after a nasty cut. (i had to pay a fee because i am not a french person, and the EHC doesn't cover "mundane" injuries like a deep cut in your finger.)
the healthcare system in the US seems like total chaos to me.