No.. your belief is wrong. The exact quote is
Quote:
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One of them's in charge at the Tower now.
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It does not even hint at any disturbance that you are assuming. This particular Nazgul must have been present at the Black gate but so what? He was still in charge. The Witch king was in charge of Minas Morgul and he went off to war to the Pelennor field did he not?