While they used Kurumi's state as bait I don't think it actually failed. I think they had two reasons for the plan. It's likely they already knew the plan would fail. Much of this manga has been quite deceptive. As mentioned that they would not be alive in the next few days and the rescue team lied about coming to them, because someone is planning to burn the city (possibly by dropping bombs) and they don't care about, just wanting to get things done. It's going to happen sometime in the next few days. As also stated that they would not be able escape it in time or out-run the destruction... So maybe the plan was expected to fail so they could delay the bombs been dropped and buy some more time to get back and save everyone. That team was unlikely going to come out for anything else and pretending to put Kurumi as bait was all part of the plan. They had their own bowman and would know if Kurumi was lying. They never stated exactly that it was Kurumi who'd survived so they won't know who to take. she said "we have someone" which is the truth. All this could be wrong. I have a feeling that the the lie detector thing maybe a bit inaccurate too as we see in some of the parts with yuki. We'll only wait and see soon.