Just thinking of the 3 times I've gone over my handle bars and none of them involved braking, one was hitting a brick at speed, one was not getting enough air to clear a jump in a messed up trail, one was a weird chain suck at speed on a cheap bike.
Hitting black ice, bad surfaces, tram tracks, etc usually results in my experience with the bike going over on one side or another, due to the the wheel being whipped out from under you again not involved with the braking.
Also involved in the art of cycling is knowing how to brake, knowing how your brakes operate on each bike. Having a nice lil' skid now and again.
Therefore I'm out