I can understand this feeling, but I guarantee that in most cases, there are things that the family knows that we don't know, and things that they have told LE over time that we don't know and may never know. Memory is a tricky thing, sometimes we think something happened one way but another person remembers it a different way. Or details come to us that we didn't think of the first time we were asked.
Neither one of the parents give me any kind of hinky feeling, because IMO, it's not fair to judge a parent in this situation without some real reason. And I mean something other than a person closing their eyes, or their voice breaking. I always ask myself, how would I come across to the public if I were thrown into a situation like this.
I see comments all the time regarding them not crying or showing emotions in these interviews. Strong emotions cannot be sustained over an extended period of time. It's been 2 weeks, the tears are drying up, the shock is wearing off, and now comes the numbness, where they are just going through the motions of being alive while their daughter could be laying out there dead somewhere. How could we expect them to stay the same, day after day? It's impossible.