Why was Boromir allowed to join the Fellowship?

[Inziladun]

Originally Posted by William Cloud Hicklin

But Boromir wasn't sent to seek allies, but to seek the answer to the dream-riddle. That he certainly found.

True, but Boromir's words to the Company seem to indicate he would have been at least a bit irritated if he had had to go to Minas Tirith alone.

'To the tall isle I will go, but no further. There I shall turn to my home, alone if my help has not earned the reward of any companionship.'

FOTR The Great River

As much as Denethor loved his son, he might have seen Boromir returning by himself as a slight, which could have turned him even more against the thought of accepting aid from anyone but the Rohirrim.

Originally Posted by William Cloud Hicklin

WRT another line of discusion: although Bormir certainly learned right off the bat who Aragorn was, that "Who" was "heir to the North-kingdom, Chieftain of the Dunedain of Arnor." That in itself did not imply advancing a claim to the throne of Gondor; a thousand years' worth of Aragorn's predecessors had not done so, even though some of them were certainly in communication with Minas Tirith from time to time. Boromir plainly had no problem with the idea of Aragorn coming to MT, seeing the Sword (and possibly the arm that wielded it) as great potential help in the war.

Boromir though was possibly looking no further than the defeat of Sauron. If Aragorn survived the war, the question of kingship could then be dealt with.
It may be noteworthy that in Boromir's Ring-delusion, he "became himself a mighty king, benevolent and wise." Maybe his acceptance of Aragorn was indeed not as solid as it may have seemed.