Vertex parent is being used here because I don't want the child objects to scale when the parent is adjusted. In theory it parents to the vertex and doesn't share in the transforms (at least is my understanding).
In the picture below the parent object is bordered in yellow with the child in orange. Before Vertex Parent is applied the two vertices line up with each other (and right where I need it). After being applied the child moves a tick to the left, halfway through the width of the plane.
The thickness of the plane itself is due to the solidify modifier (also shown). If not applied, then the child object does not move. Either way the parenting process shouldn't cause the child to move since the vertex doesn't move, correct?