You can always negotiate and threaten to not pay. They might send you to collections or even sue you for the debt, but often they'll agree to a smaller number to avoid the hassle.
Of course, that stance is in their best interest and not mine... so maybe I wasn't being forward enough?
This all feels quite ridiculous.
It honestly depends on the individual hospital. They almost always have a contract with insurance that they can't accept less, but nobody's checking and it's common for them to do so. Some hospitals are reasonable and especially if they see if you have low income/assets, will settle with you. Others don't care at all and will not accept any less and just send you to collections or sue.