Notwithstanding any other provisions of the Welfare and Institutions Code, the county which is responsible for the payment of public assistance to any person or group of persons under Chapter 2 (commencing with Section 11200), Chapter 3 (commencing with Section 12000), or Chapter 4 (commencing with Section 12500) of Part 3 of Division 9 of that code, and the needy relative in the case of aid to needy children, shall provide the necessary hospital or medical care, or both, if otherwise qualified for that care. If a recipient of public assistance moves from one county to another county within this state to make his or her home, the county to which the recipient removes shall become responsible for providing medical or hospital care or both upon notification by the first county that the recipient has moved to the second county for the purpose of making his or her home in that county, provided that the recipient is otherwise qualified for the care, except that he or she need not meet the residence qualifications set forth in Section 17105 of the Welfare and Institutions Code.