With complete respect to those whose opinions differ:
I absolutely think the parents of a missing child (especially these "missing from their beds" type of cases) should be treated as "POIs". As should anyone else who was in the home or had access to the missing child. From the first minute.
That does not mean overstepping legal procedures or harassing the parents, but they should be surveilled and questioned, vehicles should be searched, etc. Too much valuable time can pass if the parents are not immediately looked at for the disappearance.
I think (I won't say I KNOW, because who does unless they find themselves in that position?) that I would expect to be treated as a suspect/POI if my child went missing under suspicious circumstances while in my care. And as I have said before, I would retain an attorney right away. It would be the sensible thing to do and I honestly don't see how an innocent parent having representation impedes an investigation.
That said, I do think that parents who do not cooperate with LE either on their own or under the advice of counsel are highly suspect. Finding that child should be the MOST important thing and an innocent parent, it seems, would move heaven and earth to cooperate.
And by cooperate, I mean with LE. I totally get not wanting to speak to the press and they are under no obligation to tell 'us' anything. As much as we want to know EVERYTHING. And I do. I just can't say that not talking to the media looks hinky.