Because Banjo was clearly a spin-off of DKC in spirit (I know about Dream, but Banjo even first appeared in DKR), Banjo as a whole looks like something Nintendo would've created, because the games apparently used the Mario 64 engine (read this somewhere), because Nintendo is where platformers flourish and some of if not the best ones are on?
Banjo to me IS a Nintendo franchise that was robbed from them, I'd argue that Banjo would NOT exist if it wasn't for Nintendo, had the legendary partnership never had taken place, Rare would either not be the success they were, or possibly have even been shut down long ago.
Plus I'm pretty sure Nintendo had a huge positive influence on Rare, even going as far to suggest Dinosaur Planet be a SF game (for better or worse), and DP would've gone to MS had this not happened, Nintendo clearly influenced Rare, and Rare's greatest successes and most memorable franchises were created under Nintendo's wing.
Rare WAS Nintendo, those two saw eye-to-eye, had very similar philosophies, etc.
MS was the worst thing to happen to Rare, I would not be surprised if even the Stampers regret the sale (it was them who started it), Rare's biggest names sure do (Grant Kirkhope and Chris Seavor to name a few).
This is why Banjo does not feel right on the 360.