I understand EXACTLY what you wrote and the pdf you posted.
What I wrote explains why your answer is a goofball answer in the situation of a rifle fore end. Got it?
With the same weight in the same material you can make a tube stiffer than a solid rod. You will notice I stated that is a function of the fact deflection in the same material is a function of the depth of a beam squared multiplied by the width. The deflection resistance is higher in a tube of equal weight because its depth is greater...
Now, to do that the tube has to be significantly larger in diameter. A fore end is only so large. In the same outside dimension ( the ONLY valid case in a fore end) the more carbon fiber you put in there the stiffer the fore end will be, period!
If you engineered an intricate web of carbon in the fore end you can save weight and it will be stiff enough... but voids will make it less stiff, period.
