Braking power of the front is far greater than the rear. The more brake you use (front and/or rear), the further forward your center of 'gravity' moves, the more effective your front becomes, the less effective the rear becomes - meaning in an emergency stop situation your rear is next to useless.
In a braking situation the use of rear + front over just front is only of additional benefit if traction would have been lost on the front wheel.
In this instance the guy's gone over the bars, the limit has therefore not been front wheel traction, the addition of a rear brake would surely have made no difference whatsoever?
The front break is the most powerful for stopping and even Sheldon Brown details that in this article. However, I still think using the rear is important in some situations. If it is raining or icy, it can be easy to lock up a wheel when braking with a single brake. If it is the front that locks, this will almost definitely cause you to stack your bike, especially if you are turning a corner. It's up to you and you know how well you ride, but I think a rear brake is a must on all non-fixed bikes.
The front break is the most powerful for stopping and even Sheldon Brown details that in this article. However, I still think using the rear is important in some situations. If it is raining or icy, it can be easy to lock up a wheel when braking with a single brake. If it is the front that locks, this will almost definitely cause you to stack your bike, especially if you are turning a corner. It's up to you and you know how well you ride, but I think a rear brake is a must on all non-fixed bikes.