Interesting question, and it brings up another interesting question: if Boromir had been told by Denethor that Elrond was legitimate and trustworthy then why was Boromir so skeptical of Galadriel? He was almost as hesitant to enter Lorien as he was to pass through Moria!
Did Boromir not know of the close relationship and allegiance between Lorien and Rivendell? Or maybe Elrond's history of aiding the Dunedain of Arnor was known in Minas Tirith, whereas Lothlorien was more distant, mysterious, and difficult to comprehend. You'd think someone would have provided a little Elves 101 during a month in Rivendell and another several weeks' travel with Gandalf, Aragorn and Legolas ...
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