[Retroman]

All I can say is, why would anyone kill their own daughter?
[if one of the parents was a little disturbed, the chances of them both being murderers/mentally unstable is slim to none.]

Then, turn it into a worldwide event and attract endless police and people of authority, investigation teams etc? Only to draw attention to themselves and potentially get thrown in prison for several life sentences.

I think people believe they killed their own child because that makes a better story, and also gives them someone to blame instead of constantly wondering what happened.

Now if you're suggesting they paid someone to kidnap and kill their child for them, again..they'd both have to be mentally disturbed in order to do such a thing. And im pretty sure their quality of life wasn't all that bad, so I don't see what they had to gain out of it.