After reading 46 CFR 310.56(d), I think USMMA decides the waiver BUT according to standards consistent with USNA. But, please, anyone who knows for sure - we'd love to know!
Waivers. Some medical requirements may be waived for enrolled students and applicants to the USMMA who require such a medical waiver to qualify for admission and/or retention. Since commissioning in the United States Navy, or any other branch of the Armed Forces, is a requirement for graduation, no waivers will be granted for medical conditions which would prevent commissioning in at least a restricted status in the U.S. Navy Reserve. Individuals interested in waiver consideration may request a waiver by writing to the Superintendent, USMMA. The granting of medical waivers will be based on U.S. Navy guidelines and regulations for waiver consideration for admission to the U.S. Naval Academy and the physical requirements consistent with commissioning as a reserve officer in the U.S. Navy in a restricted line program. Individuals requesting medical waivers must be able to meet all other admission requirements, including the physical examination requirement for an original U.S. Coast Guard merchant marine license as a third mate and/or third assistant engineer. The decision of the Superintendent on any requested waiver is administratively final.