I find the 'un-teaching' versus 'reminding' discussion very interesting. Originally, I would have agreed with the un-teaching stance, but after reading I've changed my mind.
We actually had a recent incident that highlights this perfectly. We have a elding at our barn that came out from pasture after two years of who knows what kind of riding and was brought to us. (We eventually bought him.) Anyways, we trained him in the basics, and began cutting and sorting training on him. He had great lateral movement off his front, and a nice, deep backup. A little lazy, but laziness is easier to deal with than hotness. He was ready for low level shows- we just hadn't brought him to one yet. Come show time a good friend asked if he could ride him since his mare was due to foal in a few weeks. We agreed, though were slightly wary. The man wasn't a super accomplished rider.
Fast forward a few days later, and the horse is a wreck. He'd back up when asked, then prance, lurch, and back up more when cued forward. Any cues to turn were recognized by several steps backward, a 90 degree turn, and more backing up. He wouldn't sit still. He would go from a walk to a trot instead of a walk to a lope, like he had been trained.
Now, did he know that he was following the cue the wrong way, or was he dulled down by the bad rider?
We proceeded with correcting him. I would get him to back up, stop, then walk forward. If he backed up again instead he got the free side of a split reign on his derriere. Within five minutes he was back to normal. So I have to wonder if I was just reminding him, because he was honestly confused when I first got on.