I'm not going to get into the full on debate going on between you and others, but I will disagree with your feeling on how your hands effect, or don't effect the horse, and his behavior. Please don't take this like I'm trying to pick on you...this IS just MY observations, and experience.
I just got back from a Clinton Anderson clinic, and his main horse that was being schooled, is a horse that is always tense, tosses his head, jigs, etc...you name it, he does it. However, Guess what 'solved' his problems? Taking the pressure off his face/mouth. Most people use their hands to stop or otherwise slow a horse down. His owner admitted, that that is what she does...The horse's behavior was in his owners hands, literally. What the clinician did was simply work on bending the horse laterally, get him to move his feet willingly, and to stop when he sat down (or one reined him, if he didn't listen to his seat)...not once did he lean on the bit, or try to pull the horse to a stop...the horse calmed down, his head came down, he relaxed, and he stopped wanting to move forward everytime the rider asked him to stop...again, the horse's behavior was directly tied to the rider's hands.
So yes, a horse's behavior, whether good or bad, or anywhere inbetween can and often times will be related to how his handler handles his mouth/face (bitless). I have had horses who respond better bitless, and others, like my current mare who seem to prefer her snaffle bits to pressure on her face (bitless). Does she respond bitless? Sure, but she's NOT as relaxed, so that is what makes the difference for me...and I broke her in bitless so it's not like I didn't have time to evaluate how she performed (rope halter, as per norm for me when breaking in a horse).
Everytime I step on a horse, whether it's one I'm training, or my own mare, keep a mental check on how my hands are handling the horse...ideally the only thing the reins should 'control' are the horse's head and neck; your seat and legs are what control his shoulder, ribcage, and hips...ultimately all forward, backward, sideways, etc, movement.