Medicare Indian Health Fairness Act of 2003 - Amends title XVIII (Medicare) of the Social Security Act to: (1) authorize reimbursement for all Medicare part B (Supplementary Medical Insurance) services furnished by certain Indian health facilities; (2) require Medicare providers to charge no more than Medicare rates for inpatient hospital services provided to Indians who are eligible for contract health services from the Indian Health Service, tribally operated health programs, or urban Indian organizations; and (3) authorize outpatient or ambulatory care clinics (whether free-standing or provider-based) operated by the Indian Health Service, an Indian tribe, a tribal organization, or an urban Indian organization to elect to be reimbursed on the same basis as if such clinic were a hospital outpatient department of the Indian Health Service.