I have been asking myself the same question. I have seen people leave their child behind to finish high school when they have moved out of state. I have seen people let their child go stay with people for the summer on farms, at camps, relatives' homes, and the like. They don't file proper paperwork to my knowledge other than to give them a notarized medical release.
So if she did let Casey go stay with a "friend" for the rest of the summer without saying who...what has she actually done besides lie about it? She held the parental rights. She doesn't have to answer to her parents about letting Caylee stay with someone else...however...she does have to provide such proof to LE and be able to produce the child upon request (if I am not mistaken).