The goal of the exercise is to make you fearful, intimidated, and compliant, and to reinforce the government's dominance over you. The polygraph is just a prop. The examiner is the one really measuring you. Even if your saint's halo is still slightly visible at noon on a sunny day, you will always be given the impression that you barely passed.
So it hardly matters that a polygraph is pseudoscience, because the placebo effect is real. If you think you're being objectively measured by a machine, instead of subjectively judged by a man, that makes his job simpler.
Otherwise, it's Iocaine Powder.
(I can neither confirm nor deny whether I have any actual experience with polygraph testing, or whether I know anyone who does.)
I couldn't help thinking that the polygraph might have worked in that situation mainly because he believed it would!
Edit: maybe this also belongs in http://tvtropes.org/pmwiki/pmwiki.php/Main/ClapYourHandsIfYo...
Pity, that just about negates your otherwise informative comment.
Pseudoanonymous people posting on the Internet can't be trusted anyway, right?