Don't know whether it is indeed a useful distinction, but after having read the thread IMHO a quite crucial question is whether "stick and rudder skills" refer to a) handling an aircraft at the edges of the flight envelope (stalls, aerobatics) or b) feeling at ease flying an airliner by manually operating the flight controls and referring to raw instrument data.
While increased skills in a) certainly do no harm I doubt that putting the emphasis there would make such a significant contribution to safety. Here, I agree with Voss's initial quote. By contrast, becoming overwhelmed and falling behind the aircraft and one's current situation as soon as one has to make the usual maneuvers by hand-flying is IMHO a completely different story.
So, if "stick and rudder skills" means being able to aileron roll a 707 (or a Decathlon) I agree with the claim that "this is not about better stick and rudder skills". On the other hand, profoundly knowing and understanding one's aircraft and its systems (which is IMHO the point) would include being at ease manually flying it through the normal gaits and maneuvers, wouldn't it? Nice side effect: without the need for organizing and scheduling extra hours in gliders or aerobatic spam cans or relying on simulators that lack an authentic seat-of-the-pants feeling, b) can largely be trained and kept up to par in day-to-day operations.
BTW, I think that the outstanding performance by Capt. Sullenberger and the rest of the flight crew(!) is not even remotely limited to pure handling skills acquired in glider training (and
AFAIK the PF in the AF accident had been trained to fly gliders, too).