one of the best posts by chick, can you elaborate more on the bold part?

Sure can
Lets use the BP as an example...Used as a training tool, the correct form would be to arch the back so that I could pass my arm between you and the bench, at the small of the back...grip would be wider than shoulder width.
this positioning alone, will fix 90% of the problems...
Now...the use of a "non grip" will be crucial for the ability to use a pressing motion , as opposed to a push....you dont need a thumbless grip per se, just dont need to white knuckle the bar with an iron grip....the harder you grip, the more focus is directed to using the arms, tris and back muscles....none of which are being targeted in this exercise.
In effect, what you need to do is relax all the other muscle groups, and focus ONLY on PRESSING the weight up...not PUSHING the weight up using every muscle in your body with legs flailing about, etc...
You know why push ups are such a great chest builder? Because there is ZERO grip involved....none. same attention should be given to any chest exercise in this senario...inclines, DB, flys, pec deck, etc...same positioning, same non grip...
The "mind/ muscle" connection is basically a means of directing focus to one group while eliminating another...
I see guys doing curls, and their neck/ traps/ shoulders/ forearms are getting all the work...not so much to the actual curl itself...channeling their effort into getting the weight from position A to B...when the goal should be to relax those groups and zero in on the motion of the curl with the bicep...relaxed grip to eliminate the forearms, shoulders relaxed and back to eliminate the push from the rear delt...
Thats why you see guys heaving up the 80 lb. DBs...but dont really have big arms.