My instructor, who has her silver medal, had me sit behind the vertical as an exercise for a particular horse but it was an exercises not some place she wanted me to be permanently. I also asked this question to another instructor, as I had come in late, where a famous clinician who was having some riders do just this. What she said is that he was also doing it as exercise for those riders because they needed to learn to follow the horse and doing that(as an exercise) helps them to learn. Whether that is the case in the pictures that you saw or someone misinterpreted something that should be an exercise as something that your suppose to do all the time is anyone's guess.
Kmmoran, that is some impressive airtime in that photo!
czgm7r, I agree with your observations. I have been advised (momentarily) to sit behind vertical to help activate the core/stomach muscles. But you don't want to sit that way all the time. It CAN help someone with a less-than-active core "feel" how those muscles should be.