In fact it was quite the opposite. Most politically active colonists recognized that their quarrel was with Parliament. However, the King was still a potent symbol of power and there was a division of opinion where the he was concerned. Some of the colonists believed that George was being duped by his ministers, or otherwise kept from recognizing the truth of the situation. They constantly argued that colonial representatives should bypass Parliament and meet directly with the King, because they believed if only he knew how his subjects were being treated, he would intervene on their behalf. More radical colonial leaders believed that view naive, and thought that the long was an active participant in making policy towards the colonies.
Only after numerous petitions were sent, and turned away empty handed, did most of the colonial leadership come to accept the fact that the King wasn't going to save them, and that he sided with the government.
If you look at the literature coming from the colonies until about 1775, King George III was who they were pleading with to restore their natural English rights. However, when violence started King George III laid the smack down feeling that the colonists were being disobedient to him and his Parliament. So when you read the Declaration of Independence you see a list of things the King and the Parliament failed to do.