I took a polygraph years ago about money missing at work, and was extremely nervous and scared, but still passed, as I did not do it...
I pretty much trust them.
In any case, I sure would take one to help out a grieving parent.
I took a polygraph voluntarily to help train polygraphers. I failed it miserably, although everything I said was the truth. The mall security office was looking for people to take the test so they could train their bank of testers, and they told me never volunteer to take a poly again. I didn't even pass the part where I said what my address was.