This all makes very good sense. I'll throw my take at it, to sorta supplement the condensed information you posted. I'm sure Puhn was very thorough in his book, I've yet to read that one.

The sway bar is basically a U-shaped piece of metal, that lays "flat" against the bottom of the car, and has each end of the "U" connected to a "moving" part of the suspension assembly, be it the A-arm or the strut body itself.
When the car leans into a corner, the outside suspension compresses which wants to bring the tip of the "U" up. Well since it's also got its other tip connected to the other side of the chassis which is trying to extend, the "U" will have to twist to accomodate both movements. The larger the bar, the more resistance to twisting. Simple.
The two attachment points under the car's body are there to support the bar itself, as well as provide "bracing" to force the bar into twisting... Otherwise it would just "lean" freely and be useless. Still simple.
Now let's install that large bar on soft or worn rubber bushings. When the car leans into a corner, the sway bar has to recieve the load in order to resist it. Well if you have worn bushings that allow an 1" of deflection on each side before the bar goes metal-to-metal and finally recieves load, you're adding a "delay" to its initial action. Once all the flex has been used up in the bushings the bar will finally see load and resist further leaning of the body. You gotta remember that the bar is forcing those bushings to twist, because it's very rigid.. the thing does not want to bend! Were this a more flexible bar, the bushings might be adequate when new.
Poly bushings apply load to the sway bar much quicker. This means a smaller sway bar gets a "boost" in initial effectiveness, which is very percievable as the driver. This makes the car effectively sway less, as the initial lean required to twist the hell out of the worn bushings is taken out of the equation.
The racecar extreme to this is spherical bearing end links, which are a solid connection. The sway bar will start recieving twisting force at the first minute increment of lean that the chassis sees.
Notice I said worn bushings? OEM is very comprehensive, and the whole suspension is a system. The stock bushings are most probably specified stiff enough to tranfer load to the stock bar in a desirable manner. Poly bushings on a stock bar might bring a bit more "crispness" to the car's feel, but it won't do miracles to the leaning, against good OEM bushings. If the bushings are shot, then it's obviously another story.
Just like a stiff spring destroys a soft strut that wasn't designed to control it, a stiff sway bar will destroy soft bushings that weren't designed for it. And as proven by the very capable Aussie bar, it also finds other weak points!
Remeber the chassis attachments are there to "force" the bar into twisting, otherwise it just wants to lean. Well the Aussie bar is stiff enough that once it maxes out the flex from whatever bushings it has, it still does not want to twist, and the stock mounts are not strong enough to coax it... we all know the result.
Solution: upgrade the whole system. Larger bar, better bushings, better supports, better hardware. Strive for the comprehensive end-to-end solution, eliminate the weak points.
..and as usual, it all depends what you want out of your car. Open cockpit racecars don't use sway bars, but they have NO regard to ride quality. I didn't use a front bar on my own setup.. but there was nothing you could do to make the car ride "well" ... it was always controlled, and very stiff. No problems with lean.
Trivia: Why not take a stock suspension and install montrous 3" sway bars on it? The car would corner flat, AND could still have a soft and comfy suspension!! Is this a good idea, and why?