I cordially dislike this narrative. Its as if Jackson's artistic voice was always the problem, and his supposed inability to fully exercise it benefitted the films - which is another way to say that The Lord of the Ring was what it was despite of Peter Jackson, which is nonsense.
Its essentially a narrative which was imported from accusations drawn against George Lucas, but - when copied full-cloth to this series based on all-but superficial similarities - is completely out of place.
The fact of the matter is that every big-name director is the final word on any of his films. Do you think someone overrules Spielberg, Cameron or Nolan on their productions?
What matter isn't whether the director has the final say or not, but rather whether or not the director is the kind of person who's beyond reproach or not: which Peter Jackson isn't. He always stresses that he wants people to "come up with better ideas" than himself.
There are multiple examples when he brought up an idea, and was talked out of it by his collaborators. I think at some point he toyed with the idea of a tipsy Gandalf, until Ian McKellen talked him out of it. His cameo on The Desolation of Smaug was veto-ed by Philippa Boyens; his editor Jabez Olssen advised him to remove a line of Gollum that mentions the name Smeagol in An Unexpected Journey, etcetra.
Hell, that's why he lets actors have input on the script throughout the shoot. Because he's collaborative - not because he likes to doggedly cling to his own notions and ideas.
It wasn't any different on The Lord of the Rings, either. Technically, Jackson always had the final say, because he always had final cut rights. He overruled New Line's requests with regards to the length of the prologue, the narrator, etcetra. But he was also constantly open for input from all collaborators.
Its the kind of narrative that makes for a nice story: a up-and-rising director makes a masterpice, only for his success and hubris to bring him down. Too bad it just doesn't apply here.
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