Keep in mind this very important step: "Put the tops back on the oranges and wrap them in aluminum foil."
I tried this trick once on a camping trip. I was not told to wrap the orange in aluminum foil, although that wasn't a problem--the outer peel didn't burn, and the cake cooked nicely. Still I think it would have helped. No, the bigger problem was that I wasn't told to put the top back on the orange and didn't think to do it, so the upper part of my cake tasted like ash.
The lower part was still delicious, though.