"Rewarding bad behavior" in order to achieve good behavior was one of the hardest to understand until I realized (was told) you are actually rewarding the dog refocusing on you even if only for a microsecond at first.
I'm not sure that's exactly true. I think you are rewarding the dog and thereby changing the emotion of the circumstances. Read what I wrote here about dog growling at other dogs:
http://www.basenjiforums.com/showthread.php?t=10968
As I wrote that, I'd been sort of 1/2 @$$ed doing what I said. When I wrote that, I decided to kick it up a notch and by george if I haven't noticed improved behavior. Even from my 13 year old, Jet the trying. (Of course he also just had his back adjusted, so he's probably feeling a little better which helps.)
But with the LAT game, you do click for the dog looking at the object and then reward off to the side so that the dog must turn his head to get the reward. So the dog does have to sort of re-orient to the handler. (If the dog won't/can reorient, the dog is probably over thresh hold and you must move the dog farther from the stimuli. All of that is covered in the CU book.) Zest is great at the LATdog game however once when I was using her for a demo dog, she refused to LAT the rat terrier in class. The only thing I could think of was that normally I played LAT with dogs bigger than she is, so she didn't realize that smaller dogs are dogs too.