It looks like a ceremonial division, doing parades and the like. The "tie down" you see is simply a lead rope clipped to the bridle, run around the horse's neck and tied in a fancy knot. It's part of the cavalry traditional tack, you'll see mounted police units and the like using it. As far as the horse being ridden by people who don't ride well, it looks like the members are experienced horsepeople who train quite a bit like most drill team units.
Guess I don't see what the hubbub is about.
We grow too soon old, and too late smart.