Can the insurance company at fault deny paing for treatment to injury from auto accident?

Sure. Remember that an insurance policy is a legal contract wherein the insurance company agrees to accept risk from the policy holder according to the terms of the contract. If the policy holder does not live up to the terms of the contract then the insurance company may deny coverage. For example, if the person lied to the insurance company on the application then the insurance company may deny coverage. One of the terms of the policy is that the insured agrees to inform the insurance company of all residents of the home as well as regular drivers. If the insured does not list his 17 year old child who drives one of the vehicles regularly and lives in the house and then the child has an accident the insurance company could not be expected to provide coverage for the accident. Since the insured broke the terms of the policy which is a legal contract then the company probably will not provide coverage because the insured committed material misrepresentation and lied in a significant manner on the application.