Although I haven't had problems either way, I recently started taking less rind off, in hopes of not compromising the "power fibers". Those are the fibers right under the rind, and are what makes bamboo such a great backing. Those fibers supposedly have a much higher SG than the averaged SG reported for bamboo, like in the .8 or higher range, and have excellent bending and stiffness values.
So treat them nicely, and they will treat you nicely.