My understanding is that polygraphs absolutely DO work, but they're not that reliable, and they don't work correctly for everyone which is why they're inadmissible as evidence in any decent jurisdiction. Worse, people who are good liars and people who have trained for the test can beat it, and those are frequently the people you want to catch with the test, so all you're doing is scaring and harassing the honest people, because they get the opposite problem, that they fail the test because their nervousness shows up as lying.

So, the fundamental premise of the machine, that these physiological factors frequently change in response to peoples' thought processes brought on by particular lines of questioning, is true, but it's nowhere near reliable enough to be used as any kind of test. It'd be like a police radar gun that gives inaccurate readings for 20% of the cars, leading to both lots of unearned tickets and lots of speeders evading a ticket.