I guess the short answer is that it shouldn't matter IF your bow is well tuned and you have adequate fletching control, and the broadheads are aligned with the arrow.

I think that it may matter more with the cut on contact, basically 2 bladed heads, especially if there is any poor flight as the arrow is starting on its way. My experience of over 10 years ago sounds like what you have seen. I was shooting Bear Razorhead lites, with the bleeders removed, since I didn't want to keep breaking them in a foam target. When I had the main blades lined up vertically (I also used o rings for this), the broadheads hit dead on with field points out to 40 yards. I was very pleased, thought I had finally figured out bow tuning. About a week before the season, I thought I should probably try one of the heads with the bleeder in, just in case they didn't fly the same like everyone told me they would. At 25 yards, the arrow (which had been flying right where I had been aiming it for weeks) veered down and hit the deer target in the leg! I thought maybe I had just made a really bad shot, so I took another arrow and BH without a bleeder, and it hit right where I was aiming. Tried the bleeder again, and it veered down and under the belly of the deer. I was absolutely crushed! In cases like that, I really think the way the arrow leaves the bow can make a huge difference, especially with that type of head. After that year, I spent another year of frustration trying to get the old outsert carbons to fly with broadheads. I finally learned to bare-shaft tune, and that pretty much eliminated the problems I had been seeing. I know some will disagree, but IMO, if you can get a bare shaft to fly straight out of your bow, you should be able to shoot any reasonable broadhead well, as long as the head is aligned with the arrow (spinning straight) and you have adequate fletch control. Once that is how things are, the orientation of the head to the fletch or whatever, doesn't matter very much.