Medicaid Psychiatric Hospital Fairness Act of 2003 - Amends title XIX (Medicaid) of the Social Security Act with respect to reimbursement for specified emergency care and services of private institutions for mental diseases that are subject (under the Emergency Medical Treatment and Active Medicaid (EMTALA) Program) to certain requirements for examination and treatment for emergency medical conditions. Requires the Medicaid program to reimburse such institutions for care and services required to stabilize an emergency medical condition, the treatment for which is within the range of services that such institution typically provides, of an individual between ages 21 and 65 who came or was transferred to the institution.