If a driver of a truck towing a camper that exceeds the truck manual's towing rating is involved in an accident is the truck driver at fault?

If he was At Fault, regardless of whether he was pulling a camper or not, he would be responsible. Pulling a camper doesnt make you responsible for an accident if that was the only thing you did wrong. If someone rear-ended him, its their fault, if he rear ended someone or ran a red light, then yes, its his fault.