I have almost completely rehabbed my rotators, and alot of that was modifying my routine to exclude all exercises that maxmimized shoulder rotation.
I think what I'm trying to say is that lats are critical at the bottom, for a healthy person, or any person, moreso than the shoulders....BUT...if you have weak shoulders, rot.cuff problems, etc. the shoulders will hold you back like nothing else. The lats insert at the humerus, and adduct, extend, and internally rotate the shoulder. If all is well it works together, but if your shoulders are weak, the entire chain suffers.