Originally Posted by makeinu

A good grip is not necessarily a tight grip. A good grip is an unobstructed grip that allows you to apply the right amount of force for the situation. Putting brake levers between your hands and the handlebars hinders that. It might even force you to use too tight a grip (for example, lightening your grip might prevent you from squeezing the levers with enough force to skillfully engage the brake).
Which is exactly why it's a bad idea to either commit your hands to braking by putting them over the brake levers or commit them to steering by putting them under the brake levers. Using different extremities for braking and steering allows you to switch between the two more quickly, but if you are stuck being committed to one and can't switch fast enough then you might be tempted to do both simultaneously because you can't do either one with the necessary precision..