With Saddlebreds, a lot of people consider the rack as a "trained" gait. Very few Saddlebreds do a natural 4 beat rack without schooling. They have the natural inclination to learn, and the genetic ability to perform it. Often you will see babies rack along after their mothers as it is easier to keep up, but they are predominant trotters. We had a few colts who took a few months to become comfortable with their trot. It is the horse, ultimately, who decides if he would be better off as a three gaited, or five gaited horse. Some prefer the rack over the trot. Some are never taught the cues to rack undersaddle. But if they are to compete as a five gaited horse they must perform a walk, trot, canter, slow-gait, and rack.
Are you sure the Arabians you saw were performing a true four-beat(each foot hitting the ground independently) lateral gait?