I've never experienced it on a bike, but I have on skateboards back when I was a kid.
I drive a manual transmission car with a real high (rpm) first gear. Usually in stop and go traffic I'm in 2nd gear but sometimes it's bad enough that I stay in first. When in first, I barely hover my foot over the gas pedal to give it a super steady amount of pedal pressure. My foot remains very steady and sure. I should mention I also have bumpy (custom sport) suspension. When hovering over the gas pedal in this way going real slow, it takes only the slightest bump in the road for my foot in relation to the pedal to change which causes the car to jump a bit. That jump (even when I purposefully don't move my foot to compensate) will continue as the car adjusts for the slight change in throttle and when it winds back down again it gets repeated because now the car slows and my stable foot hits the pedal again.
I think this is a very similar phenomenon. By the way, the only good way for me to break the shimmy is to give it more gas or use the clutch. I've learned that trying to control the shimmy by modulating the pedal directly is pointless and makes it worse.