Why was Boromir allowed to join the Fellowship?

[TheLostPilgrim]

Boromir had made it kind of, well, obvious at the Council that he did not see harm in using The Ring? Even if he was somewhat quelled by Elrond, his first thought was to use the Ring for strength and as a weapon, and he even said he saw some wisdom in Saruman's desire of it.

Knowing as they did the Ring's corruptive power, why then did Gandalf and Elrond allow Boromir to join the Fellowship? Surely they could've seen his weakness and his lack of true understanding--That this man was a soldier, a leader of men, a brave warrior and nothing more--Not one of the Wise or who truly understood how dangerous or evil the Ring was? An overly proud and perhaps desperate man who would desire of the Ring to save his land?

Did neither of them foresee the possibility of him becoming a threat, since he did not truly understand the peril of the Ring and even before setting out already had desire to use it, if only for a noble purpose?