BC, think of a Gyroscope. You try to turn it one way and it reacts by angling to another direction. Our wheels, at speed, are gyros. Get a wheel bouncing up and down, it can develop motion side to side. Company I worked for gave me an old Econoline to drive on a project. It was an early 1970's generation, not even the one before the current E-Series. If I went over a railroad crossing at 45-mph I had to come to a near stop before the oscillation stopped. Till then it felt like it wanted to shake the steering wheel out of my hands.
Shouldn't happen unless there's wear/play in the steering/suspension and my old Econoline had plenty of that. Still, not ready to say it can't happen with a tight suspension, at least to a degree.