I agree that it makes no difference which way the fibers are oriented, because silk as a woven backing doesn't work. I very firmly believe this from bows I have built. If the bow survives, it would have anyway. Silk has no part in saving it as a woven fiber. I have built bows with questionable backs that held up for many shots before I decided to silk back them. I have also built bows that I thought were fine and backed them for looks only to have them break.
Aside from my opinion from exerience above, here is some science for you. The silk fiber is supposed to take the tension load of the back. Tension loads run the length of the bow. Therefore to do any good, so must the silk fibers. Otherwise they will not take any load off the back. It would be like gluing bamboo at a 45º the the back. No good, just adds weight. You need the silk fibers to rn the length of the bow.
Now notice I wrote silk does no good as a woven fiber. But it may work extreemly well as individual strands laid down like sinew. When I use jute or hemp backingsni unravvel the string into its indidual fibers and lay it down in hide glue. Now THAT works amazing...