Quite like that, my friend. The case of Yang Kurama is totally the opposite to the Yin beasts, since Yang Kurama searches for the opposite to mantain balance, this is, Yin.
Dark Naruto = Yin.
Yin is darkness, the femenine, the imagination, the mind.
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Now then...
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Dark Naruto has more insight than the Naruto we know, Dark Naruto was the Darkness, The Yin that Yang Kurama was searching for.
Well, the thing is...
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That quite explains why Kurama didn't detect "the trueself" of the Jinchuuriki when Naruto fought Kurama.
Kurama was very interested in the Dark Side of Naruto, the original Yin that resided inside him, the one who built hatred in the chapter 1 of Part 1.
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The one hidden in the darkness, the one who wasn't aknowledged until Naruto confronted him in the Falls of Truth.
Pink note:
Look what a mindless bird can do when it have 'instincts' (Yang):
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