Too much engineering, not enough practical experience. Overtightening is the way to waste a perfectly good headset! You will preload the bearings and then the first added load (from a bump in the road) will Brinnell the bearings (dent the races). Now you have an indexing headset, making steering nearly impossible. This happens all too often when people try to adjust a headset properly, much less overtighten it. The best way to adjust a headset is from loose to not loose, rather than from tight to not tight. A precision headset like Campy that is installed accurately will still have some preload when adjusted from tight to not tight. You just can't feel it because it is so smooth.
I don't believe that the adjustment of the headset is key to shimmy. It is as Brandt says, a product of the entire system, you and the bike. I do believe that a bike with less trail (less than, say, 50mm) will shimmy easier than a bike with more trail. It makes a squirrelier handling bike (hence my comments on my old Raleigh International that started this thread) which causes you to not only overcorrect but to grip the bars tighter in an attempt to control the shimmy, thereby propagating it. We have deraked the forks on a number of Internationals ( and Treks, and other bikes) over the years to minimize their shimmy.
A load on the rear of the bike doesn't help either. In the case of my International, I had it heavily loaded on an old Karrimor rack which had no triangulation to make it rigid, which allowed the load on the rear to be a tail wagging the dog.
If you didn't pick this up somewhere else in this thread, the ways to overcome shimmy if you encounter it are first to relax your grip. The tighter you grip the more it shimmies. Especially if it is cold outside and your arms are very tense. Then to touch your knee to the top tube. This damps out the spring (remember it is you and the bike) and stops the shimmy.
Bob Freeman
Seattle