New Horizons slingshots past Jupiter

New Horizons has received it's gravity assist from Jupiter and is on it's way to Pluto. I was surprised to see how far from Jupiter the probe actually passes. When you think of a gravity slingshot, it seems that the probe would be grazing the surface to get maximum acceleration, when in fact it's still outside the orbits of the Galilean satellites at closest approach.

New Horizons set a record for fastest transit time Earth-to-Jupiter of just over a year.