Fair Trade in Pouch Tuna Act of 2003 - Amends the Harmonized Tariff Schedule of the United States to eliminate tariffs on pouch tuna imported from member nations of the Association of Southeast Asian Nations (ASEAN) (Brunei, Cambodia, Indonesia, Laos, Malaysia, Philippines, Singapore, Thailand, and Vietnam), excluding the Union of Myanmar, up to the quantity of such duty-free imports from beneficiary nations of the Andean Trade Promotion and Drug Eradication Act. Restricts eligibility to those ASEAN nations that provide and enforce internationally recognized worker rights and environmental protections.