When the professor administers the lie detector test to Paul he has Paul describe the alleged kidnapping in the narrative. Polygraph tests are only administered in the form of a series of yes/no questions, never narrative descriptions.
Professor Alderson extols the infallibility of the lie detector test. As a criminology professor he would have or should have been aware of Frye v. United States, decided 40 years prior to the air date, in which the Supreme Court explicitly ruled that the systolic blood pressure test, an early form of lie detector, was not sufficiently reliable to serve as admissible evidence. In the 40 years between decision and broadcast, and indeed through the present day, the Court has not overruled this opinion or allowed any later form of lie detector evidence.