So why is it only certain bikes have this issue?

You guys are giving good ideas to mitigate it once it happens, but hard to believe the rider is the one starting it in the first place.

I used to ride sitting upright with no hands for hours. One day the same bike started shimming when no hands for no apparent reason. Resting a knee, still no hands, damped the oscillations. some years later it stopped doing the shimmy.