Gandalf a "steward?"

[Boromir88]

davem, I agree to an extent. According to the rules set down by Pelendur and the Council, Arvedui's claim was illegitimate (which the law itself they made is what was illegitimate. They found a loophole and they took advantage of it. Politics and power will do that. )

The loophole in Arvedui's claim is he claimed to be Isildur's heir, and was restoring the High Kingship. Where the Council found the loophole that Isildur forsook his Kingdom:

The Council of Gondor answered: "The crown and royalty of Gondor belongs solely to the heirs of Meneldil, son of Anßrion, to whom Isildur relinquished this realm. In Gondor this heritage is reckoned through the sons only; and we have not heard that the law is otherwise in Arnor.~Appendix A: Of Gondor and the Heirs of Anarion

And we are told that:

But soon he departed, and after he had given counsel to Meneldil, his brother's son, and had committed to him the realm of the south, he bore away the ring, to be an heirloom of his house, and marched north from Gondor by the way Elendil had come; and he forsook the South Kingdom, for he purposed to take up his father';s realm in Eriador, far from the shadow of the Black Land.~The Silmarillion: Of the Rings of Power and the Third Age

This is what the Council uses to deny Arvedui's claim. The law was illegitimate, and aside from our opinions about that law, this was the law Gondor had made and Arvedui's claim was illegitimate. But there's a difference between Arvedui's claim and Aragorn's claim.

Arvedui claimed to be Isildur's heir and was restoring the High Kingship. The Council said, na can't do that because Isildur gave up his rule here (even though if we are told he didn't), but still that's what the Council had made law. Aragorn claimed to be Elendil's heir and was restoring the High Kingship. Aragorn was probably aware of Arvedui's claim being rejected, so all the more important to claim to be Elendil's heir, who indeed was the High King, and restore that Kingship. Where Isildur (again according to the Council) had relinquished his rule in Gondor and was not the High King, he gave up his rule in Gondor and went to rule Arnor.

Aragorn most likely knew about Gondor's ruling in Arvedui's claim, hence the importance of claiming to be Elendil's heir and not Isildur's. Which I think makes it look as if Aragorn's claim was in accordance to Gondor's law.