H-D made big changes to the stiffness of the touring bike chassis in 2009 and again in 2014. The bikes are much different and better now. The bottom line is all bikes wobble, hopefully in a safe and controllable way.
You can affect it a lot by how you load your bike, adjust ride height, handlebar selection, and tire pressure. Here is a brief description from Wikipedia:
Wobble or shimmy begins when some otherwise minor irregularity accelerates the wheel to one side. The restoring force is applied in phase with the progress of the irregularity, and the wheel turns to the other side where the process is repeated. If there is insufficient damping in the steering the oscillation will increase until system failure. The oscillation frequency can be changed by changing the forward speed, making the bike stiffer or lighter, or increasing the stiffness of the steering, of which the rider is a main component. While wobble or shimmy can be easily remedied by adjusting speed, position, or grip on the handlebar, it can be fatal if left uncontrolled.
The top five influences on wobble have been found to be lateral stiffness of the front tire, steering damper, height of bike center of mass, distance of bike center of mass from rear wheel, and cornering stiffness of the front tire.
An academic paper that investigated wobble through physical experimentation and computer modeling concludes: "the influence on wobble mode of front tire characteristics, front frame inertia and chassis stiffness were shown. In particular, it shows that by increasing front tire inflation, chassis stiffness, and front frame inertia about steering axis and decreasing side slip stiffness of front tire, wobble mode damping is improved, promoting vehicle stability."
