Hi Kevin,
Some more context: My A/R is a 65cm frame and has 700c wheels and Berthoud 50mm stainless fenders. I was probably running 35mm Paselas back then, though I've experienced it with fatter tires as well. My feeling is that the load affects it more than tire size. (Lateral oscillation of the fender may have contributed to the shimmy.)
I think I had a densely loaded Riv big boxy handlebar bag and a small Nitto rack with all sorts of stuff strapped to it on the front and a big Nitto rear rack with large panniers and a sleeping bag and tent strapped on top (Or maybe the tent was strapped on the front; I don't remember, as it was nearly 20y ago)
The shimmy I experienced would happen when I tried to ride no-handed or one-handed with a very light touch. The tendency to shimmy increased with front load and decreased with speed, and I never experienced the shimmy that Mike mentioned at high speed...and I like to descend fast! I don't think I ever had any shimmy with both hands on the bars.
FWIW, I am not able to ride no-handed, even with no bags on the bike.
I hope that helps!
Cheers,
Andrew in Sydney