He is a "true" Assassin; he was trained and accepted by the Assassins. Him being a Pirate doesn't mean he's not a "true" Assassin.
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Edward was cool in that he chose the creed purely out of faith in the code Altair was born in it Ezio and Connor kinda joined partially out of revenge and necessity Edward joined because he believed in the code from the start (not that the other assassins didn't believe in the creed they totally did ) he is basically the opposite of Altair at the beginning of assassins creed 1 Major spoilers [spoiler]even Torres admits this in the end when he says that his ideals suited him[/spoiler]