“County organized health system” means a health care organization that contracts with the State Department of Health Services to provide comprehensive health care to all eligible Medi-Cal beneficiaries residing in the county, and that is operated directly by a public entity established by a county government pursuant to Section 14087.51 or 14087.54 of the Welfare and Institutions Code, or Chapter 3 (commencing with Section 101675) of Part 4 of Division 101 of the Health and Safety Code.