A symmetric head won't tend to twist in the cut, there is a light asymmetry in the forces applied because the wood is compressed against one side and just pops off on the other, but this is generally small compared to the direct force against the blade.
Shingle splitting axes are designed to compensate for this (flat on one side, chisel ground on the other) since the different compression forces on each side will be much more pronounced when just splitting thin sections off a log.
[Axes] are also really wide if you look at the bit to poll distance which makes them very difficult to turn.
If the edge is in line with center of mass and the grip (image a lightsaber, or whacking something with a small diameter rod), then there is no tendency to turn at all (although to be honest I haven't used a lightsaber).
One of these days I'm gonna have to send my lightsaber for a passaround. Any interest?
Cliff, I also find myself wondering how the width alone makes a blade difficult to turn, though I do agree with you about a round grip vs. one more oblong in cross section.
I think there are really two different things at play here in regards to "twisting in the grip", but I'm not really sure how to explain my thoughts, and I'm still thinking it through; I may be wrong.... perhaps "geometry" and "mass". The further the edge is from the centerline, the more leverage the wood will have against the blade to turn it. If the mass is distributed further from the centerline, it can make the blade want to twist easier if that mass is asymetric, but will keep it in line better if symmetric.
If the edge makes contact behind the centerline, as in striking with the tip of a scimitar in kal_aa's example, then the geometry will want to keep the blade in line. Likewise a strike with the tip of khukri will want to twist out of line.
But with mass, let's compare a viking sword with a wide central fuller against a sword of equal width and mass that's hollow ground with a thick central ridge. Since more of the mass is concentrated near the edges on a viking sword, it will resist rotation better and "track" straighter in the cut. (assuming we could negate any difference in the way those geometries interact with the target material)
In kal_aa's example of the scimitar, he seems to be assuming a strike at the tip. The center of mass is still above the grip though, so with a strike closer to the hilt, the edge may be below the center of mass, making it want to twist more. I have seen certain Polish sabers where the knuckle bow was made from very thick & heavy steel, which would bring the center of mass down closer to be in line with the grip. I believe this was actually done to change the sword's dynamic handling qualities, but would also help in this cutting example. Note the one pictured below also has a horizontal thumb ring. By getting part of your grip further from the centerline, again you have more leverage to resist torques in cutting and induce them in maneuvers. (and the torque likewise has more leverage on your thumb, which could mean a broken/dislocated thumb during a violent wrenching.)