Patrick, the dynamics of a bow and atlatl are totally different. No experience with the atlatl personally, but it's not hard to guess that orientation probably has something to do with hanging weight. Stiff side down to counter this?
With bows comes handles that we have to get around. Perfect world there would be no stiff/weak sides to deal with. But when it comes to the orientation of shoots arrows it's the total package of stiff/weak sides plus their idiosyncrasies, undulation, crooks, humps, bumps, kinks and what have you. The latter you deal with first in orienting the shaft, then orient stiff/weak sides. This may put the strong side against the bow or down on the shelf/hand. But the weak side should never go against the bow and/or hand.
Just for general information, we mauled over this subject in great length on the old PA board and this concept has been proven to many to be accurate over the years...........Art