Bananas produce ethylene gas which accelerate the ripening process in a variety of fruits - including bananas themselves.
Placing them in the fridge allows the gas to build up and hence accelerating any ripening in the bananas and other fruit in the fridge. Keeping them out will allow the gas to disperse more readily.
For the same reason you should keep them seperate from other fruit rather than in a fruit bowl. Banana hangers are good as the keep the fruit away from others and ensure it does not bruise under its own weight when very ripe