ok, so you define something that isn't understanding (symbolic manipulation, use of a magic rule book).
But where do you define what it is? "grasping what a symbol refers to" is another way of saying "understand" - it doesn't define what it means to "grasp".
Just imagine a perfect rule book that already has a translation from one language into the other for every imaginable sentence, some native speakers just have written any possible combination down. You could 'translate' by just visually picking without having any idea of what's being said. They understand, you do not.