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All of my tests are done on a PC. This game will take any controller it recognizes, and try to attach its moves (not only) to Xbox controllers, but also any controller, based on generic notations (like POV, Axis, Button 1, Button 2, etc). I don't necessarily mind these impositions per se, but, if I can't disable this automatic recognition, I have a problem with that.
Traditionally, PC games would have separate Keyboard and Joystick modes. If this game had that, you could use the Keyboard mode, and then create a controller profile (with something like JoyToKey) and get total control over your controller layout, down to the last button. This would work for even REALLY weird controllers, like racing wheels and flight sticks.