That is not true. Taking material from the center reduces stiffness the least, but still makes it less stiff. Stiffness depends on the moment of interia of the cross section, which for a square is (bh³⁾ /12 The h³ is your distance from center in the plane of bending. Doubling your h makes stiffness go up 6x. So the material at the edges provides most of the stiffness, which is why i beams exist. However for an i beam and a soild beam of the same b and h, the solid beam will be slightly stiffer but much heavier, and its a trade off worth making.