Checkers you are right, my trainer did show the other method with the dog circling around the person completely. In our class, we had used treats andin that case it seemed much easier for the larger dogs where their noises were up higher towards the people hands holding the treats
With Cody being so short, it was easier for me to do it on the left side as you described.
I still take treats with me when walking Cody - I don't give them as much.
I just put them in a fanny pack along with my cell phone; and potty bags bags.