Donkey Kong Land (GB)
Basically the Kongs intentionally let King K. Rool steal their bananas again to prove to Cranky Kong that they can take them back on a 8-Bit-System too.
Granted, story doesn't matter for a Donkey Kong game. But even as a kid I felt insulted by the totally stupid backstory back in the days. The game would have been better off with no backstory at all.
edit: when I think about it, I don't know it that qualifies as a story twist. But it felt that way when coming from Donkey Kong Country. =P
Official member of VGC's Nintendo family, approved by the one and only RolStoppable. I feel honored.