Im pretty sure for them to both bw capturable you have to choose one and then lie about the cure.(the red text) when they ask about the cure. After a few days they run off and you can capture them both. This doesnt really affect your status with them more rather gives a heart to the person you saved. And yes they will be able to controll it when you cure them and can change of free will. Logan doesnt have anything that shows that but bernard does