This whole concept of the importance of having a strong grip relates to what is called Muscle Irradiation. Muscle irradiation simply means that if you want a muscle to contract with more force, than you must contract the surrounding muscles with more force. More technically, it has to deal with how the nerves are integrated in our bodies and how it creates a kinetic chain of impulses.
For example, my strength coach back in high school always preached the concept of never taking a thumb-less grip while benching, not just for safety reasons, but because he wanted us to grip the bar with as much force as we could possibly achieve, because when we applied a strong grip to the bar it would activate a kinetic chain for all the other muscles to contract with greater force, starting from your forearms, working its way through the triceps, shoulders, and then into the chest. Because of your grip working harder, everything else had to as well.
Here's a good way to prove this point;
Go stand in front of a mirror, turned to the side so you can see your arm. Clench your fist while trying to keep the rest of your arm relaxed...you can't do it. Once you clench your fist you will notice your tricep also contracts.
Just a little tid bit. Sorry for the rant.