That Saddlebred mare is not all that unusual for a SB. Some SB bloodlines carry that gene quite prominently. The breeders I have talked to say it comes from breeding like to like with the emphasis on the shoulder laying back to an extreme to get more 'lift' on the front feet/legs. Oddly enough, they do not seem to have much pain or discomfort as long as they are not asked to carry heavy riders.
I have a 4-H member with a very sway backed gelding. This gelding was not born this way but has aged way beyond his 17 years. They fill in the gap with small pony pads, put a big, thick on top of them and ride him everywhere. He has been to state 4-H shows several times and goes on many all day trail rides. He does just fine at that level.