Pat -- actually, they are less apt to rear. A horse rears when you let them stall out and slow down. Moving forward faster keeps all of their feet on the ground. When they are moving forward, they just cannot rear.
We find that rearing is a much bigger problem when people let the horse stop and then argue with it about letting it turn around and leave the scary place. People that are as fearful as the horse, usually tighten up, try to 'hold' the horse from turning, try to get the horse closer so he can look at the scary thing and, in reality, set the horse up for spinning around or rearing and then getting more fearful.
Letting a horse stop and look just sets them up for more stopping and looking and more fear reactions. Keeping the horse 'responsive' and busy just does not give the horse time to be reactive. It just works so well to keep them busy and moving.
I hope this clears up the confusion. I could have been a little more articulate.