No comment on whether or not this parent is involved.
However, I would never, ever, take a polygraph. Snake oil. The guy who created the Wonder Woman comic book created the “lie detector” as a PR stunt for his comic book. It is a good intimidation tool but it does not detect the truth or lies and can be used to portray truthful people as liars.
I have friends who are attorneys and they all say they would never let their clients take a lie detector test.