Fudgy,
I'm note sure how familiar you are with the effects of corrugation. Please forgive me if I am telling you what you already know, but you can demonstrate the benefit with a plain sheet of paper.
Grasp the paper at one of its edges and try to hold it so that its flat surfaces are horizontal. The paper will simply fold down and hang vertically.
Now fold the paper into a series of small (about 1/2 inch)corrugations. You will now find by grasping the paper at the ends of the corrugations, it can be held with its (now corrugated) surfaces in a horizontal position. The corrugations have made the paper stiffer in bending in that particular direction. This is because any bending across the corrugations requires a greater degree of stretching and compression, than is required with the plain flat sheet.
By corrugating the surfaces of the flying controls, the designers achieve the required stiffness, without resorting to heavy internal structure.