I'm sure there are nightmare situations in both countries.
My story: when pregnant with dd, I returned to the USA for the final 3 months of the pregnancy. I intended to pay for the cost of birth out of pocket, but wanted insurance as back-up in case something went disastrously (and expensively) wrong. I found I was unable to purchase private health insurance to cover me for the birth, as the pregnancy was deemed a 'pre-existing condition'. I was therefore, declared 'uninsurable'.
I then trotted down to the local government health offices, and after several meetings/appointments and filling out papers (yes, it was a pain), I was declared 'insured by the state'.
Fast forward to the day of birth - I went to my hospital of choice to check in. I was ushered into a huge, clean, newly decorated private room, gave birth 12 hours later (given an epidural half-way through and a caesarean due to worryingly high blood pressure). My own GP delivered the baby, and I spent 4 days in hospital recovering from the birth.
Cost to me? A big fat ZERO. I couldn't have been treated better. The big irony was that I could have paid (and orginally intended to), but because of my inability to secure insurance, the government program took care of everything.
Mine is a happy story, which I thought I'd share to balance out the horrir stories.