EXACTLY!!! The first thing *most* parents would do, would be to clear themselves so the focus can go to finding where their daughter is and catching who may have been involved in their disappearance. But see, someone with something to hide wouldn't take a lie detector test - because they'd fail and they don't want to go to jail.
It would be a very rare occasion that I would permit a client to submit to a polygraph. An innocent parent may be one of those rare occasions. Otherwise, there is no reason to subject yourself to a polygraph, innocent or not. Taking one is a lose/lose proposition. If you fail, LE says the tests are reliable and you are lying, even if you're innocent. If you pass, LE says the tests are not reliable and you're still a suspect, even if you're innocent.