Motor Vehicle Rental Fairness Act of 1999 - Amends Federal transportation law to prohibit a State from holding motor vehicle rental or leasing companies liable for harm caused by a person to himself or herself, to another person, or to property resulting from that person's negligent operation of such motor vehicle. Declares that such prohibition does not apply to liability imposed under a State's statutory or common law based on negligence of a motor vehicle owner. Declares that nothing in this Act supersedes any State law: (1) imposing financial responsibility or insurance standards on the owner of a motor vehicle for the privilege of registering and operating a motor vehicle; or (2) imposing liability on such companies for failure to meet financial responsibility or liability insurance requirements under State law.