No, that is not what the law says. North Carolina law says that you do not get paid for missing work the first week but you begin getting paid the second week. If you miss the third week – or if you get a rating to an injured body part – they have to go back and pay you for the first week.
If you do use vacation or sick time for that first week the insurance company is still obligated to pay you for the first week if you meet the eligibility for it. While they may claim that this is double dipping or a windfall to you that isn’t how the law sees it. You are using up a limited resource – your vacation time, sick time, or personal time off – and thus you didn’t get it for free. Oddly enough we see this misinformation coming from CorVel and state and local employers quite frequently.