If the owner of a motor vehicle is one whose vehicles are operated under a permit or a certificate of convenience and necessity issued by the State Corporation Commission or the Department, proof by the owner on behalf of another as provided by this chapter may be made if there is filed with the Commissioner satisfactory evidence that the owner has complied with the law with respect to his liability for damage caused by the operation of his vehicles by providing the required insurance or other security or has qualified as a self-insurer as described in § 46.2-368.