The finance lady got my insurance information and then told me that they do this to make sure that they're being completely transparent about all the. Then she told me that my portion would be $12K. I called to check with the insurance since that certainly didn't seem right and they said $5,400. The hospital emailed me a second estimate that said my insurance should cover 100% with nothing out of pocket from me, which also doesn't seem accurate.
So... Maybe I owe nothing, maybe $5,400. The only thing I'm sure about is that 12K is way over the out of pocket max, so that woman was up in the night.