While this may be helpful for business people and politicians, I think this isn't great advice for this demographic. A huge skill lacking within this industry (and of course I'm generalizing) is that of verbal communication. Wouldn't talking more, much like writing more, help that skill?
Silence, like body language, is an essential part of "verbal communication skills" - that's the point I'm making. You can no more learn "verbal communication" without learning to use silence than you can learn "driving skills" without learning to look in the rear-view mirror... (poor analogy, but you get the idea)