Hospital as referred to in this section shall include any institution within the definition of hospital in § 32.1-123. No hospital, as defined in this section, shall be immune from liability for negligence or any other tort on the ground that it is a charitable institution unless (i) such hospital renders exclusively charitable medical services for which service no bill for service is rendered to, nor any charge is ever made to the patient or (ii) the party alleging such negligence or other tort was accepted as a patient by such institution under an express written agreement executed by the hospital and delivered at the time of admission to the patient or the person admitting such patient providing that all medical services furnished such patient are to be supplied on a charitable basis without financial liability to the patient. However, notwithstanding the provisions of § 8.01-581.15 a hospital which is exempt from taxation pursuant to § 501(c) (3) of Title 26 of the United States Code (Internal Revenue Code of 1954) and which is insured against liability for negligence or other tort in an amount not less than $500,000 for each occurrence shall not be liable for damage in excess of the limits of such insurance, or in actions for medical malpractice pursuant to Chapter 21.1 (§ 8.01-581.1 et seq.) for damages in excess of the amount set forth in § 8.01-581.15.