"Personally, if I were innocent, I'd take it and figure that I'd "pass" it and that would be all the cops needed to focus all their energies in another direction."
Well that's the fun part about lie detector's. Depending on who's side you're on you ignore the flaws. He passed it so now we get to show that Lie detectors rarely even have a 50/50 percent accuracy rate. Or that they can be beaten or point out that moons weren't aligned properly before given it to him. But if he were to fail it, that would be your smoking gun. He failed the test, game over case closed.
The best advice is to usually avoid them. Don't take them unless you have to (security clearances come to mind, but that's a little different)
I agree about the lie detectors, as there are good reasons for why they are inadmissable.