I think Tate's "try to pull the bar apart" cue serves to do two things:
1) Grip the bar primarily with the inside of your hands - i.e. that nice little spot formed by making a circle with your thumb and index finger. In SS Rip says that you should angle your hands out slightly for your bench press grip, and you do this by first gripping the bar with just the thumb and index finger, and then wrapping the rest of the fingers around the bar. I like to do it Rip's way, just because I find it to be a more specific and consistent cue than just "try to pull the bar apart".
2) Grip it tight. A tight grip helps maintain tightness throughout the whole body.
To each his own. Whatever cue works for you, run with it.