The only thing that comes to mind for me is maybe the parents are frustrated to continually see them searching the woods around the house when they think someone has her and has taken her farther away. Maybe they think LE is wasting valuable time and that's why they drove off in a huff. They are in a position of having to entrust Baby Lisa's life to LE and if they think the focus is off and time is being wasted maybe they were furious and some argument with LE followed causing them to disengage from LE?
This explanation makes total logical sense. This type of argument would produce the same reactions we see here on both sides.
It does not explain to me the WHY in the LE calling an immediate emergency type press conference. As another poster noted earlier, this kind of squabble usually is kept close by LE. They usually do not like differences like these to be batted around by press. HMMMMMMMMM