I don't think it's stupid for Jack to trust her. They've been through a lot together and they've formed a bond. The survivors know nothing about their time together, I think the rest of them are right to not trust her, but I can understand why Jack would. They're basically alienated from their respective groups now and they've risked a lot to help each other out. Yeah Juliet is a liar and manipulator, but I don't think she's evil and instinct and conscience tell her to work with the survivors, but whatever baggage she's carrying from her past and her relationship with Ben makes her feel obligated to continue helping him. So Jack really isn't stupid for that. He's just stupid when he comes up with a great "plan" and has to make a decision. He's an empathetic character but a bad leader. I think Sayid should officially be made leader or at least have a triumvirate of Jack, Sayid, and preferrably Locke, but since he's bleeding in a mass grave, I guess Sawyer, Sun, or Desmond would do.