We've encountered similar situations (especially the "NOT A BILL" fuckery) and the "oh don't pay it when it arrives because insurance is always slow" shit - but luckily none of our three births have been that bad cost/handling wise, even though we used three different hospitals (same insurance).

The smaller hospitals in general have been better but it's so obviously a giant clusterfuck.

I can't even imagine how someone without partner support (who the hell wants to deal with hospital fuckery post-partum) does it.