It might be a myth, but for consistancy sake it doesn't hurt to have all the broadheads orietated the same. It just rules out that one possibilty. However, more info would be nice such as bow weight and draw length, arrow length and spine rating. It could be the arrow spine is marginally on the light side. You could do something like turn the bow weight down about 5# and find out.
Olfatguy mentioned spin testing the arrows which is a good point. There should be no wobble of the broadheads. Just a few thousandths can make a difference in this respect.
Tuning of the bow could be a contributing factor, too. Maybe it's not tuned just just so. Don't rely on just paper tuning. Try several different methods just to be sure.
What kind of fletching and size is being used? Maybe there isn't enough drag on the back to properly stabilize the arrows.
Are you possibly torquing the bow by gripping it too tightly?
These are all little details that should be looked at and it might not be just one of them, but a combination of many. They all work hand in hand.
Hope this helps give you some ideas to work with.