Why was Boromir allowed to join the Fellowship?

[Inziladun]

Boromir's words at the Council could have been taken at face value to have come of simple ignorance of the Ring's corrupting influence, and a product of the state of the man's life, as you describe. Since he did apparently accept Elrond's explanation of why the Ring had to be destroyed, maybe they thought that was sufficient. Note too that it wasn't until Gandalf's fall that Boromir began to show further outward signs that he was still having thoughts of using it.

Also, Boromir had made the journey to Rivendell alone, and it was really miraculous that he made it. Since the Fellowship intended to travel back towards the general direction of Minas Tirith, and Boromir was obviously going to head there himself, it would have been a dishonor toward him to have not included him. And slighting the son of the Steward of Gondor when a war with Sauron was brewing was something to be avoided.