I tend to both agree and disagree with the author.
Really, it all depends on what you're trying to accomplish. In example: Football players, (particularly those who are on the defensive end) are going to need that extra "pushing or shoving" power which comes from the chest area and that's one of the primary reasons they put so much of an emphasis on maxing-out on the bench during training.
It would be extremely unsafe for a football player to try and max-out on a fitness ball with dumbbells because number 1, a fitness ball can only handle so much pressure from weight. But second of all, if the ball pops due to an overload of weight placed on it, they probably would've been better off risking getting injured on a flat-bench than having nearly 550 pounds of momentum pulling them down with their backs and the backs of their head hitting solid ground.
On the other hand, athletes like boxers don't need to worry about putting on excessive weight on the chest area because the mechanics of the punch should derive from pushing off with their legs and using their hips correctly.
So again, it obviously depends what your goals are and if it truly is conducive towards what you're aiming for as an athlete.
Speaking of conducive training, you guys may wanna check this out: tinyurl.com/train-like-its-your-last
P.S. If you're opponents got you in something like a "full mount" for example, you probably aren't going to be trying to be "pushing him off of you" with your arms most of the time. You'll be so entangled that "pushing" really isn't going to do you much good. Therefore, why try and "push" him off of you when you can be more effective by up-striking or by trying to get him into some sort of a submission hold from the bottom? Just a thought.
Wish you all the best.