Here it's implied that sprouted sweet potatoes are edible because they are not from the same family as potatoes (it's like saying arsenic is fine to eat because it's not from the same family as lead)
Are sweet potatoes with green sprouts still safe to eat? Sweet potatoes are botanically unrelated to the common potato. Potatoes are part of the nightshade family while Sweet Potatoes are cousins of the morning-glory. They do not produce the toxic solanine. source
and here it's also claimed that you can eat the sprouts itself (even though there's a lot of junk-science on the site):
The sweet potato sprout tastes very similar to spinach. Its nutritional value is also comparable to spinach. Spinach however, must have its seeds planted and you'll need to wait for over two months each time you harvest it. In the case of sweet potato vines, you can harvest it practically every 2 to 3 days per branch.
I recommended this practice to all my brothers and friends three years ago, and most of them are now enjoying following my idea. All of them including their families claim that their blood test results are in normal range and their cholesterol levels have never been abnormal since then. They very much enjoy eating sweet potato sprout salad. source
So I'm curious, is it safe to eat a sweet potato (with or without its sprouts) or are both these sources incorrect in claiming so?