It seems a lot of these dilemmas are only dilemmas if you believe one person can be morally responsible for another person's actions. In the case of "Jim", for example, if he kills the one person, he will be morally responsible for that person's death. But if he refuses, he will not be morally responsible for the death of the twenty - the executioner will. Nothing about Jim's refusal forces the executioner to kill, and the executioner is still free to choose not to execute anyone.