If face planting was uncommon, why was the word invented in the first place? It has been widely used by bicyclists, probably dating back to the 1970s-style suicide levers.
I have a hard time believing that your center of gravity is lower when your hands are on the tops. How can moving your hands farther forward and lower (from the tops to the brake hoods) cause your center of gravity to go up?
Hybrid bike riders don't face plant much because they generally ride more slowly than road bikers. Also, their center of gravity is farther back and the wider handlebars stabalize the upper body. Still, I am sure they do face plant from time to time, especially when going downhill.