The Illegitimacy of Aragorn’s Claim to the Throne

Was Aragorn the legitimate heir to the throne of Gondor? Pure gold for any LOTR geek. 

I have to disagree with the conclusion though. My main two reasons for believing Aragon was the true King were the facts that:

A) Elrond believed him to be King (and he knew Aragon's dad). In fact believed him enough to allow Aragon to marry his daughter Arwen (not something he'd do for some ordinary mortal slub).

B) the King of the Dead recognized him as the true King and Aragon was able to release the dead and hold their oaths fulfilled. That's something only the true King could have done.

I do agree that the political succession process of Middle Earth was batshit insane. But was it any more batshit than making whoever can pull a sword from a stone king or be granted supreme executive power just because a watery tart threw a sword at you?