Look to be honest I'm getting bored by a discussion that's going around in circles so this is my last reply. We all know grass is green don't we? It may be dark or it may be light, but it's natural color is still green. And wether color blind or not, grass remains green. How did it get this complicated? Besides, the real meaning of that comment is that there's not a whole lot of point in arguing about the definition of a standard term used in positive reinforcement training throughout the world. Some may think it means something else, but those that know better; know better.
Cherie as for your scenario, I'd do the same as you are doing. I'd signal for the required response and if I didn't get it I'd bring him back and ask again (consistency) until I got even the slightest hint (small step) of the right answer. I'd click and treat after just a few steps. I don't stop the horse to treat, the sound of the click ( I use my tongue not a plastic clicker) tells the horse he is allowed to stop and will be rewarded at that time. He turns his head laterally and I will reach down slightly to give the treat. I allow about 10-15 seconds of 'dwell' time (rest) and then will continue to ask for a little more each time, reducing dwell time as he catches on. If he should take the wrong lead after I give the signal I would again bring him back to try again. No click/treat. Only correction.
I'm finding it hard to grasp how the horse would be confused under these circumstance as you say. If that's the case then there are a great many confused horses out there. Some seen at Olympic and professional performance level. In fact positive reinforcement training has the opposite effect on a horse that you claim. They aren't confused and distracted, they are focused and on target. That's the whole point. Moreover, I'd say that are equine companions are a great deal more intelligent not to have the relief that comes from being left alone compromised in any way, shape or form.