I am not even sure I agree with the article written by Mr Brown. I do not doubt his experience or knowledge, but would never tell ANYONE to brake only with the front wheel in any situation.
I fall back to what I learned from motorcycle instruction, as it applies to bicycles just as well.
Front brake is 80% of your braking power, back is 20%. In most situations the front brake will do most of the stopping, and the back brake is much like an indicator. If it skids during stopping you should modulate slightly on both in order to eliminate the skid from the back end. In any situation where you are making a low speed turn, or in wet conditions, the back brake should be applied a bit more than the front. Your stopping power will be lessened, but so will the possibility of loosing traction on the front wheel and going down.
Really has a lot to do with feel and experience. Over application of the front brakes pushes your center of gravity too far forward and makes you unstable on the bike. Aside from that, the mention above about a back up brake in case of failure is golden.