I'm pretty sure that palming off "sweet potato greens" as a vegetable is in the same camp as spiderplanet's report of a CSA pickup that included "carrot greens" along with a typed sheet attempting to convince the customer that this is a real thing. There are lots of greens that CAN be eaten if you are desperate to prevent scurvy, but that doesn't mean it is worth crunching on the woody stems instead of buying some spinach. Ish.

And no, sabotabby, do not eat those potato greens, or the nasty sprouts that grow out of the eyes of overripe potatoes. I don't think they are drop-dead poisonous, but yes, in the nightshade family. As are tomatoes. Don't eat tomato leaves either. They smell terrible enough that I don't think most people would try, but they can't be good for you.