I summon a skeleton with a command block using the following command:

/summon Skeleton ~ ~1 ~ {Equipment:[

,{},{},{},{}],Attributes:[

]}

This gave me a normal looking skeleton with a bow. I switched to adventure mode and the skeleton charged straight at me as if it had a sword. However, wielding a bow, the skeleton did no damage. It did not shoot its bow even when I attacked it to provoke it into shooting me. I repeated this experiment but with a "normal skeleton" by typing /summon Skeleton, but got the same result. Even skeletons from spawn-eggs and in survival mode, they never fired their bows.