So do tomatillos!
I didn't know if you could do this or not, so I cut off a kidney bean stem about 3 inches long and stuck it in a glass of water. A week later we had this:
Eventually I will make a chart of what roots from stem cuttings and what doesn't and how long everything takes.
The online Grow'Em Plant Propagation Database notes that you can do this with Lima Beans, but Kidney Beans are not in their index.
It is useful for me to know that plants which tend to outgrow the AeroGardens, such as beans, tomatoes, and tomatillos, can be pruned back and new plants started from the cuttings. This gets new plants started somewhat faster than starting from seed, and also, if the seedlings get too leggy, sometimes the cuttings branch out and become more attractive plants.