The online list I've used for induction (usually can't find my book handy) does not seem to include beans (either green or sting)...
http://www.atkins.com/Program/Phase1...thisPhase.aspx
Botanically, legumes include all beans, peas, lentils, and peanuts, as well as a number of inedible species (wisteria, locust). Nutritionally, people are typically referring to the actual seed when they say something is a legume. Chinese cuisine includes the use of tender pea greens (the shoots) and I don't think Atkins would characterize that as a legume. String beans are basically skinny green beans, usually with underdeveloped beans, and therefore more like a vegetable. The same is (usually) true of Chinese pea pods (the flat kind, not sugar snap. BTW, I've grown Chinese pea pods and if you let them mature, they look more like the snap pea pods).
Anyway, that's a possible source of confusion and why I suggested that eating young pods would likely follow the spirit of Atkins, even if they aren't on the list you use.