I can definitely see what you two are talking about. Shear strength of a stand is a completely diferent matter. Of course, when finishing your stand, the additional plywood will solidify the stand to and horizontal movement and possible twising. But, with the additional 2x4s in the corner, I have found the 2x4 stands to be very sturdy. When you are installing the vertical supports, I recommend gluing and screwing the two together to ensure that there is resistance to horizontal movement. When I have built previous stands having the second 2x4 in the back made all the difference in the world. The second 2x4 in the front is just icing on the cake. If you built it as pictured and attached the verticals together, I think you would be hard pressed to get it to really move.
As always, you can feel free to add additional bracing as you see fit.