Boromir is indeed NOT the only member of the Fellowship to die. Gollum (Sméagol), though not an original member of the Fellowship, dies during the War of the Ring. Additionally, if considering all who joined the Fellowship's quest, Gollum's death is significant. However, among the nine original Fellowship members, only Boromir dies - making the statement "False" technically correct if strictly counting the original nine, but this is ambiguous.