The traditional practice of using rotational motion as the principal attribute of coherent vortical structures in the buffer region of near-wall turbulent flow is shown to create a biased accounting of the role of vorticity within the structures. Vorticity associated with rotation is given a favored consideration against vorticity that is equally strong but not associated with rotation. Using data from a highly resolved direct numerical simulation of channel flow, it is shown that describing the structures based on the properties of the rotational field leads to a distorted view of the actual structures that are present. As a practical matter, this means that where hairpins are typically considered to be the flow structures, a more accurate description of the coherent events is that they are elongated mushroom-shaped vortical objects ejecting over low speed streaks. In this, hairpin-shaped rotational regions are embedded in the lobes of the mushrooms.