BigE: You're right that the two aren't exactly equivalent, but I don't think it's for the reason you describe.
Let's take an ideal boot/binding/ski system, and let's say I edge my boots to a 45 degree angle. A perfectly torsionally stiff ski would be at 45 degrees everywhere, from tip to tail. A torsionally soft ski will still be at nearly 45 degrees under the binding, but as I go towards the tip and tail, the angle will decrease.
Now let's take the same ideal system, edged to 45 degrees -- but this time we'll say the binding is torsionally soft and the ski is still ideal. This would cause the angle of the entire edge to decrease, not just the tip and tail.
In both cases, though the ski isn't doing exactly the same thing, the skier has less edging power. In fact, the first system, with the torsionally soft ski, will have better grip under the binding than the second system, with the torsionally soft binding, will have anywhere!
I agree with you that they don't have the same cure. However, both cause the skier to lose edging power and control. My hypothesis, restated, is that the loss due to a torsionally soft binding (vs. a torsionally stiff binding) can exceed the loss due to a fat ski vs. a narrow ski.