(a) To the extent prescribed by this chapter, a county is liable for health care services provided under this subchapter by any provider, including a public hospital or hospital district, to an eligible county resident. A county is not liable for payment for health care services provided:
(1) by any provider, including a public hospital or hospital district, to a resident of that county who resides in the service area of a public hospital or hospital district; or
(2) to an eligible resident of that county who does not reside within the service area of a public hospital or hospital district by a hospital having a Hill-Burton or state-mandated obligation to provide free services and considered to be in noncompliance with the requirements of the Hill-Burton or state-mandated obligation.
(b) To the extent prescribed by this chapter, if another source of payment does not adequately cover a health care service a county provides to an eligible county resident, the county shall pay for or provide the health care service for which other payment is not available.