Actually, animals are highly selective as regards what they eat. For example, there was a Nature documentary on killer whales hunting grey whale calves and they would only eat the tongue of the calf but leave the rest. Lions in the wild do not, apparently, eat the whole carcass but leave the faeces alone.A rabbit would likely have to be skinned. I am sure, though, that carcasses were left out to age for a while so that they could be more easily dealt with minus flint-knives, in more ancient Palaeo times.