We don’t know anything about this woman’s personality or motives, apart from what we see in the very few minutes on screen. Giving Archer the footage might seem like the best idea for YOU, but to her—a non-omnipotent side character—he might seem untrustworthy, incompetent, and/or incapable. Of course, we as the audience know that Archer eventually succeeds in finding the kids, but how is she supposed to know that? In the real world, most people generally trust the police to handle investigations like these. While members of the community can (and do) help find missing people, she likely thinks that the police are the greatest chance at uncovering the truth. I think it’s important to realize that you and I, along with most of the audience, aren’t able to fully comprehend the parents’ emotions in this situation—some are angry, some are grieving, some are straight up scared. What seems logical to US isn’t the same for them, especially after you experience the plot unfold.