My take is that the only use polygraphs have is to trip someone up like they did Jessie. Whether they pass it or not almost matters none. But can you trip them up by telling them they failed. That is one of the many problems with Jessie's "confessions" because of his mental faculties, he was more susceptible to being tripped up regardless of guilty or innocence.
I guess I'm a little suspicious of these polygraphs, especially when Allen says he'll use the polygraph to clear up any suspicions, weak police work if you ask me.