The expenses necessarily incurred in the support of persons charged with or convicted of a crime and committed to the county jail and the maintenance therein and in other county adult detention facilities of a program of rehabilitative services in the fields of training, employment, recreation, and prerelease activities, and for other services in relation to criminal proceedings for which no specific compensation is prescribed by law are county charges. However, nothing in this section shall preclude or prohibit the county from receiving reimbursement from a provider of medical insurance coverage for the provision of medical services to a prisoner or detainee received by or held in the county jail or other detention facilities, in those instances where the prisoner or detainee has private medical insurance coverage.