Liability to pay the hospital what insurance does not cover

I would appreciate your legal advice on the below scenario:

I gave birth in a hospital on May 16. At the time of discharge, they did not ask us to pay anything and said it was covered by insurance.

After more than a month, they called us saying they made a mistake and only half of the bill was covered and asking us to pay the balance.

Are we still bound/liable to pay after discharge?