One thing that I've noticed is that people who think Jessie was telling the truth cite his multiple confessions. However, there's actually a good reason.
At one point they tried to move Jessie without telling his attorneys before being stopped. Now, if anyone REALLY thinks that's the only time LE tried to talk to him they're deluded. They could EASILY have met him off the books later and offered him a deal (i.e "you wanna see DADDY and SUZIE again right? Well if you play ball than maybe you just might. But you have to confess everything Jessie.")
Given that Jessie had been convicted and was in a special ed class it would have been childs play to manipulate him.