I believe that at the Council of Elrond, Boromir just wasn't convinced the ring was evil. Isildur died before it could corrupt him, Boromir never actually saw what it did to Smeagol, Bilbo and Frodo had the ring for years and they looked all right. Only when it tried to corrupt him, did he believe.
I always feel so sorry for Boromir...I am glad that Tolkien gave him a heroic ending, even if he did fail in resisting the ring.