That's funny! Even some of my I-don't-care-about-horses friends know the difference between a saddle seat class and dressage.
I have watched several Saddlebred shows. When Saddlebreds become aggravated, alarmed, taken out of their stalls, or over-gingered, they naturally side pass across the ring. I definitely think that they would make excellent parade/dressage horses. This would be a great reform to the Saddlebred industry. That old tradition would become modernized.