[The Squatter of Amon Rûdh]

That's what I thought: Boromir seems reasonably happy with Aragorn's leadership of the Fellowship, but that's not the same thing as accepting his sovereignty. I've a feeling that once they arrived at Minas Tirith, Denethor would have flatly denied Aragorn's legitimacy and Boromir, like a dutiful son, would have supported him, especially since to do so would be in his own interests. It could have been very messy.