Some sobering video of what NOT to do towing

Trailer sway is actually a pretty complex dynamics problem. I did a search once and found a couple of papers which concluded that FEA modeling was needed to analyze it properly.

The key though I think I s to be sure your rig is self damping, as there are always going to be random lateral force inputs (sudden maneuvers, air pressure from a passing truck, etc) which can set off sway. To be sure you’re self damped, you can very carefully apply a steering input while you’re running down a straight traffic free stretch of highway. Your rig shouldn’t oscillate more than one cycle before returning to straight and level. If it doesn’t then move weight forward in the trailer and/or remove it from the rear of the trailer.

Personally I do this test without sway control, the add sway control for an additional margin of safety.

Originally posted by Colt So, ..... what kicks off the swaying? Once it starts, it looks uncapped and just grows.

In an aircraft, it's known as divergent instability. In an improperly designed, or improperly loaded aircraft, a small oscillation can turn into a large oscillation because aerodynamics and weight & balance contribute to the problem. It's not too different when towing a trailer. 

It is always better to arrive slower and alive than dead and in a box.

+1 to offgrid and GlueGuy.  Also of note there was some pretty aggressive driving in many of these crashes.  Failure to yield, unsafe lane changes, excessive speed, and a basic lack of courtesy in driving.