The thing about the parents is there is just so much suspicion around everything that's been done. The way they remained quiet while they're son was missing. The fact that they waited until LE had basically left the scene to actively search for their son.
I do think that CL and RL were doing what they thought was best for their son, and sometimes what someone believes is right doesn't always line up with what the majority thinks. And that's okay. Taking out everything else, I just cannot fathom sitting at my home day after day and letting other people search for my child when I reported them missing.
Even if LE had told them they couldn't participate in the search for whatever reason, contamination of a scene, concern over potential tampering with evidence if any was found, I would have been at those search locations every day.