At least Renee's mom bought that story at first. Probably just grasping on hope that everything will be okay, but she did. Julie's mom had no fighting chance. Most likely immediately drowned in guilt for allowing Julie to go, scared, all alone with this, and even if she would get this idea... maybe with Wilson's support - maybe. But most likely Fran would stomp them to the ground within first 15 minutes of hearing about this.I wish one of the other girls parents would have went to FWPD and pressed charges against Rachel for kidnapping. It would have just been a technicality but it would have set things in motion. It would have forced their hand, the locals and the Feds.
Not technicallity IMO, Arnold's took all the attention from the very beginning and started setting the narrative. They likely would be more conerned with appearances than with search at that point. On top of that there is no telling that FWPD would accept that attempt while having such a convenient scenario in the note.