In addition to the nice working Western jog, there's another kind of Western jog--sort of the analog to a horse being pulled "onto the bit" by cranking his head in, in dressage. It's a horrid gait, dragging with the forehand and creating lots of impact concussion. But it *looks* pretty, at least if what you're looking for is slow, with head tucked down and in. And it's unfortunately noticeably common.
It is *not* a proper Western jog, not any more than the trot in dressage with the head cranked in. It's achieved by trying to get a horse to do a Western jog when he's not up for it; either he's not being asked properly or he doesn't have the strength for the collection required. It is pretty bad for the horse, because he ends up pounding his legs on the ground from a bad angle; impact concussion directly for the bones & tendons/ligaments, plus the angles of impact are stressful on the joints.
It's a stretch, but if you're thinking that you've heard that jog is bad for a horse, that might be what they were talking about.