Fairness to All Fallen Vietnam War Service Members Act of 2003 - Directs the Secretary of Defense to study and report to Congress: (1) to identify veterans who died after October 31, 1955, as a result of military operations in southeast Asia whose names are not eligible for inscription on the Vietnam Veterans Memorial; and (2) on the feasibility and equitability of revising the eligibility requirements to be more inclusive of such veterans or of creating an alternative means for recognizing them.