Cannot speak for the Long Haul Trucker specifically. But I had a 1991 Trek 520, their touring bike. It had a steel frame with skinny tubes like the LHT. I never experienced any wiggling of the frame descending mountains at 40 mph with front and rear panniers, handlebar bag, and rear rack bag. I tend to think all bikes are more than stiff enough for anything. People who complain about stiffness of a bike says more about them than the bike.
I am going to have to respectfully disagree with you--sometimes it is the bike and not the rider. Most sub $2000 touring bikes are sold to people who never put panniers on them and the bike companies know that and cut corners knowing that they can get away with it. I work with a guy that owns a 520 which is slightly older than yours (old enough to be 27" instead of 700c), and he has had wiggle issues. Neil Gunton over at CrazyGuyOnABike has owned several bikes that have had ride issues when loaded down with panniers. And I have had wiggle issues with my first touring bike, a Bianchi Volpe. I am confident that all three of us were capable of getting the weight in our panniers balanced, that we know how to spin our pedals smoothly, and that we make sure that our wheels are properly seated, true, and round.
I may have misspoke when I talked about frame stiffness. I can make my Waterford frame flex, but vibrations immediately dampen out. I will have to talk to my mechanical engineering buddies to find out what material property describes the ability to dampen out vibration. I don't know how Waterford does it, but it is a beautiful thing. Sad thing is that I would expect every touring frame to do that. Cheaper touring bikes might weigh more and do come with crappier components, but they ought to be tour ready.
I am glad to hear that your 520 works for you. And I glad to hear about those glowing LHT testimonials.