There is another reason I can think of why 3 or 4 adults would cover for each other, and that is if they were involved in illegal activity, e.g., drugs. I've already mentioned this. But, I was also thinking of Trista's comment regarding Justin's claim that Ayla broke her arm while he was carrying her into the house with a bag of groceries. Trista couldn't understand why Justin was carrying Ayla because she can navigate stairs on her own.
My thought is...what if the adults in the household gave Ayla a drug to make her sleepy (and maybe gave some to the other kids, too, unless they were already asleep) so they could have "some adult time" (ala DB) and, while under the influence of that drug (off-balance and disoriented), Ayla continued to wander around the house and fell down the stairs. If that were the case, even though she "accidently" died in a fall, the adults would not want LE involved because of the drugs -- not only those in the house (they needed time to remove them) -- but also the drug in Ayla's system. Without a body, LE could not know that there were drugs in Ayla's system when she fell. Basically, in that scenario, all of the adults are culpable so they are all covering for THEMSELVES.