I don't know too much about the situation with Kyle and Jackie O, and the mother who made her daughter answer questions while attached to a lie detector, on live radio. My two cents is directed towards the lie detector, and how accurate they are. Wikipedia has some info on it. The subject has also been looked at on the show Lie to Me, which is about a facial expression expert who consults for govt and private companies to determine the truth about certain things.
Lie detectors can tell you when someone is anxious, but they can't tell you what they're anxious about. As is shown well in the clip above. It is no different from the egg.
My take is that this should not have been done. Josh Thomas's take seems to be the correct one to me. What mother in their right mind would subject their daughter to this?