The idea of keeping your elbows up & out is to give you more control and leverage. Since you do more than just turn the handle bars to turn, keeping the elbows up & out allow you to use your upper body to lean the bike instead of just your forearms. It also aids in keeping the wrists straighter. The proper way to grip the bars is similar to reaching for a doorknob, if you try this approach, keeping the elbows where they belong will be easier and feel more natural. There was a thread some time back asking why some riders have their levers up so high, gripping the bars like I mentioned you'll see why they do.
Like anssi said, your arms will reduce the amount of shock that transfers from the bike to your body with the elbows up too.