True, we know none of the things you listed.
But, I disagree when it comes to LE, and what they do or do not know. As for the part regarding a parent in this situation following the advice of LE, and if it's in their best interest or not...I strongly disagree. Too much time has passed for that, plain and simple. In the beginning, yes. Now? No. What LE has been doing aint' workin'. Time for another approach. IMO.
At this point, nearly a month later,... I say LE, or anyone for that matter would have a VERY difficult if not impossible task of trying to get a Mother or family to sit back and just WAIT, silently if they believed their child was still alive. The only way I can logically see that happening is if the family, Mother, Father, etc is sooo emotionally distraught that they don't have the energy or ability to do otherwise. Or, if they have a blind trust in LE. Which to me, is a very scary thought.
If a parent truly believed that their child was being held hostage and alive some place for almost 30 days, would they really sit by, patiently and hope for the best, after ALL this time?
Do I think a family should give up hope? No, not by any stretch of the imagination. But, sit by and do nothing. Most families would not be able to sit still, let alone by quiet. Case history is a shining example of that.
After almost one month missing. I see no benefit in remaining silent. None what so ever. Let LE remain silent with their facts, but as a family...you do what you have to do. And, I'll leave it at that.