Any child residing in the state of Missouri who has a physical disability or special health care need, who is in need of services because of his or her condition, who has been certified by a physician of his or her choice as a person who can probably benefit from such services, who is financially unable to pay for such services and whose parents, guardian, or person legally chargeable with his or her support is unable to pay therefor shall be entitled to such services without charge, but if any person, firm, corporation, or public or private agency is liable, either pursuant to contract or otherwise, to the parents or a recipient of services on account of personal injury to or disability or disease of the recipient of services, the service is subrogated to the right of the parent or recipient to recover from that part of the award or settlement an amount equal to the amount expended by the service for services which are not otherwise recoverable from the parent or recipient. The acceptance of services from the service constitutes acknowledgment of subrogation rights by the service, and the service may take any and all action necessary to enforce the subrogation rights. Any such child who, or whose parents, guardian, or other person legally chargeable with the support of the child, is able to pay a portion but not all of the expenses for the required services for the child, shall be entitled to the services if the child, parents, guardian or other person legally charged with the support of the child shall pay such amounts thereof to the hospital and physician as the child, parents, guardian, or other persons legally charged with the support of the child are reasonably able to pay.