First of all I can not believe you are having this much trouble with your insuarance company. Turn it over to them and let them handle it. Personel experience, my wife was backing up at work, a young lady pulled up behind her knowing my wife was backing out of her spot and it was still considered my wifes fault and my insuarance paid the claim, plus her rental car which was more than the damage claim! Looking at the damage of your car I would say the person backing up was speeding?