Was it legit?

[Boromir88]

This suggests to me that there was some shady dealing going on. I think that Arvedui's claim is valid. And Aragorn's would certainly be valid, because the line of the King dies out completely, so he would be the closest with the highest claim to the throne.~Eonwe

I definitely think one side was twisting things around...

The Council of Gondor answered: "The crown and royalty of Gondor belong solely to the heirs of Meneldil, son of Anarion, 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."

Arvedui: "He did not relinquish his royalty in Gondor, nor intend that the realm of Elendil should be divided for ever."

(bolding mine)
So one side said he did relinquish his throne, the other side says he didn't, obviously one is lying. Though I would think of all people the Council and Pelendur were the ones lying in the Silmarillion...

For [Isildur] forsook the South Kingdom for he purposed to take up his father's realm in Eriador.

Forsook meaning to give up, or renounce. So, what did Isildur "renounce" well the South Kingdom, Gondor, his royalty.

I do agree with Arvedui that Isildur did not mean for the two kingdoms to be divided, I actually think he probably was going to take up the High Kingship of his father. However, does he ever get to do this? As we know he's ambushed and killed. If not then the Council appears to have made the right decision in Arvedui's claim.

We also must recognize the difference between Arvedui and Aragorn's claim. Arvedui claimed to be Isildur's heir, and the Council says, aint gonna work because Isildur gave up his reign here. Aragorn claims to be Elendil's heir, taking up the high kingship and reuniniting the two Kingdoms. Which, is I think the big difference between Aragorn's claim and Arvedui's claim.

But, I have to wonder, along with Kuru, was it more of Aragorn's "claim," or the fact of his timely arrival on Pelennor, saving Gondor, and the political vaccuum in Gondor that caused him to get the crown?

Pelendur and the Council did not, in my opinion, have the authority to change the laws of succession.~Formendacil

Well, they did have the power, clearly as we see in Arvedui's case. Did they "technically" have the power, I don't know. But, clearly that's what they did, and I think it was Kransha who did a thread similar talking about Arvedui's claim, the Stewards seemed to have the power whether they willingly backed down to the claimed King or not. My understanding was, if Faramir hadn't been such a good guy and did the right thing in letting Aragorn take the crown, he could have told Aragorn no.