Don't pay unreasonable bill to hospital. Hospitals always charge much more. Think about how much those damn doctors earned. Since all documents were signed by your mother in law, you are free to any responsibility. You even don't need to reply this kind letter, just telling postman there is no such a person at this address.
Only chinese people take such kind of stupid responsibity. Look at our salary check,and we have already paid too much tax for this kind of thing. At the next time, when your parents go to hospital, you even don't need to show them any ID and tell them the right name. Tell them they just moved here, no valid ID and give a temporary address. This is method that one of my american co-worker told me.
Good Luck,