I'm going to have to say that I think Trissacar isn't entirely off-base by thinking stretching a horse can improve jumping. A lot of horses can be stuck in certain parts of their bodies and anything we can do to help them free up those parts, makes for a better moving horse. With the amount of transitions, gridwork, etc, you can accomplish something better, but with horses who are stuck in their shoulders per say, still won't reach their full potential if they remain stuck.
I have been working with a haflinger pony who is the world's best pony, goes over anything without breaking rhythm. Naturally. But until I freed up his shoulders, he lacked the ability to rock back and balance himself up. He just dove down, and the jump was awkward.
I didn't stretch him in the way Trissacar mentioned, but doing in-hand lateral movements to free up his tubular little body made his over-all movement and jumping improve by over 50%.
Same idea with the stretching, freeing up those places so that horse can use himself to its full potential.
So I think everyone has good valid points in this thread, Trissacar too.