I'm not sure specifically which 'nearly normal family' true story you are referring to. There could be many stories with such a title. It might be about a family that appears normal on the surface but has some unique or hidden aspects to their lives.
I'm not sure specifically as I haven't read it. But generally, it might be about a family that seems almost normal on the surface but perhaps has some unique or unexpected elements to their story since it's a true story.