I brake in corners all the time and I've never even come close to having an accident as a result. It's all about your technique and knowing yourself and your bicycle and how they behave together. It is not a good general rule to say "never brake in corners." Sometimes it is necessary, and if you don't know how to do it when the need arises, THAT is when you get into trouble.

Descents can be terrifying if you are not "one" with your ride. Most accidents occur when riders exit the envelope of control and don't know what to do to get back into it. A close second is failure to have a "Plan B."