What is my liability for my father's medical bills incurred during visit to the US?

Liability for Parent's Medical Bills Incurred During a Visit to the U.S. I live in California. Recently, I sponsored my parents to visit the US. Three weeks after their arrival, my father got very ill and ended up in the ICU. He had an emergency surgery and several other procedures. He has been in the hospital for 7 days. The problem here is the medical insurance issue. He has a travel medical insurance. The insurance company does not have a representative in the US and because of that the payments to the hospital could be significantly delayed (maybe by few of months or even more). Since I am not sure how reliable those oversees insurance companies are, my question is - am I liable for the hospital and the doctors expenses after my father leaves the US? If the insurance company delays the payments, or if it does not cover all the charges, or if it refuses to pay, can they go after me? I have not signed anything in the hospital. I'll appreciate your advice on this matter.