When I'm measuring my food, I like to shake it, so I can fit more in the measuring cup without increasing the calorie count. ;) Oatmeal will pack down quite a bit with some shaking.
The title is funny. I realize it's sometimes hard to translate and summarize scientific results for the layperson, but the paper wasn't comparing stirring or shaking. They compared rotating the container to tapping the container. Rotating is, ironically, a type of shaking, and closer to shaking than tapping. I would expect a good deal of dice packing in this experiment using vertical shaking, as opposed to lateral tapping.