It was irrelevant

Whether or not nat killed ben was irrelevant to their survival. If ben was alive, he would have told the birders everything the girls had done to him and each other, including the force feeding, the achilles tendon slice, holding him captive, eating javi and Jackie. Now that he's dead the birders obviously stumbled upon something they can't walk away from. The yj would not have let them live either way. Except.. if they had shot ben like they were originally going to, they likely would have ate him but they probably would not have put his head on a stake. That was to punish nat for her betrayal, not to punish ben. They would have ate him and probably had the ceremony, attracting the birders anyway but without the gruesome display that they couldn't just attribute to eating ben from starvation. So, akilahs vision was wrong and by keeping ben alive they ruined their chances of escaping