From what I know such a bill won't lose its validity. I can understand your frustration and it sounds very strange that they should call in a bill after such a long time but I don't think there's anything wrong with what they did.
I think in the end, unfortunately, you'll have to pay the bill or reach some sort of compromise with the hospital. I suggest you explore the option of settlement since they'll have an interest to close this story sooner rather than later and believe me, they're not interested in legal battles.