I think the hospital band is another piece that supports her giving the baby up to the couple. The hospital band has her name on it-Johnson-not Logan's or any other father's last name. I honestly think she could of told the couple and the baby broker that the father is not part of their life. I think the broker and the couple would think it was less risky if there wasn't a caring father involved. Who would come look for him or want him back? I do hate that it was left in the room though like it meant nothing, trash.