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Tarkin was always an exception to the 'norm'.
Even during TCW, when Tarkin was in command of the prison that was holding Ahsoka before her trial, not even Anakin could override his standing orders, despite holding the higher rank(Generals outranked Admirals.)
And like I said earlier: even when Tarkin was still just a standard Moff/Governor, he didn't give a single flying f*ck what "Vizier" Amedda had to say, and routinely told him to f*ck off... Unless Amedda was delivering a message directly from Palpatine himself, obviously.
Moreover, in the early days of the Empire(again when Tarkin was just a standard Moff/Governor), Palpatine made it clear that Vader had control over everyone in the Empire, and could 'discipline' them however he saw fit... Everyone except Tarkin, that is.
No other Governor/Moff/Grand Moff in the Empire's history ever held the level of authority that Tarkin did.