I think there is proof against this theory.
Statement #1: Naruto converts Kurama's chakra to each shinobi type, in order to share it.
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Of course, as a particular case, Naruto converts Kurama chakra to his own type to use it.
Statement #2: From Statement #1 logic says that Naruto is the only one who can resonate with Kurama's chakra correctly, but... To further strongify my statement, I use this.
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This is the chakra used for KCM. Naruto states that this is Kyuubi's chakra, one that is aparted in a sector of his body, and as you can see, it is sealed in a barrier. This means that even if this is Kyuubi's chakra, it is not linked to the Kyuubi, ergo, this sealed chakra is now Naruto's chakra type.
Statement #3: Naruto can't enter Bijuu Mode without Kurama's aid. I'm sure Kurama states somewhere that Naruto can't win without the beast chakra (Ch 611).
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Statement #4: Gaara was not the first Jinchuuriki to be captured, so the whole thing about order of extraction is disproved directly with this statement. Zetsu only said the thing about the Ichibi because it was the weakest of all bijuu, so it would be easier to capture.
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The only thing that actually makes sense about all of this is the fact that the Jinchuuriki and the Bijuu keep a connection after the extraction that let them do Tug-o-war (Ch 652).
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Conclusion:
#1, #2 and #3 proves that the source of BM and KCM are not the same. KCM uses a seal, BM does not.
#4 and #3 should suffice to create a definite proof against this theory. Order of extraction is meaningless to Gedou Mazou, and Naruto lost Kurama's avatar (the beast manifestation of bijuu mode) after the Kyuubi's reserves were used. Meaning that no Beast = No more chakra... since Kurama was the chakra provider.
If Naruto had some Kyuubi's chakra aparted in his body, that's all he can use: KCM. Bijuu Mode won't be possible without the beast.
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tysoncs, your theory is good. But you need to clearify or refute my points to win more credibility.