A public agency or private organization, or a subdivision of such an agency or organization, that is primarily engaged in providing skilled nursing services and other therapeutic services, such as physical therapy, speech-language pathology services, or occupational therapy, medical social services, and home health aide services. It has policies established by a professional group associated with the agency or organization (including at least one physician and one registered nurse) to govern the services and provides for supervision of such services by a physician or a registered nurse; maintains clinical records on all patients; is licensed in accordance with State or local law or is approved by the State or local licensing agency as meeting the licensing standards, where applicable; and meets other conditions found by the Secretary of Health and Human Services to be necessary for health and safety.