Polygraphs are not admissible in court (posisible spoilers)
The fact that the mother was subjected to 3 is absurd.
There is a reason that polygraphs are not admissible in court--because they detect changes in the body, they do not detect lies. There is no certifiable way to detect deception, even if you are micro expression expert, Paul Ekman. At best, without evidence as was the case here, you can make a reasonably informed GUESS.
What I took away from this documentary was the underlying need that people possess to create a narrative. The FBI detective (who, my God, how did she get the job?) desperately needed the narrative of the mother to be proven as a perpetrator.
"Nicholas" needed the narrative of an abducted 13 year-old who was really borne of a his sister's desire to create the narrative of a returned relative.
Humans tend to look for patterns and arrange chaos to bear semblance to order. These were people in crises (Frederic included). Chaos is disorder and the compulsion to impose order on it makes sense. We build the stories we WANT to unfold and play the characters we NEED in order for this to happen.