As the video shows, a bounced landing can snatch away control of the aircraft almost faster than you can blink. The only real defense is to brief it on approach if it's a possibility and have a plan ready, because you will have zero thinking time once it starts.
By comparison, Capt. Sullenberger had an eternity to consider his options and make his decision.
And the best pilot in the world can get dropped on the runway if a gust knocks 13 knots off the airspeed at just the wrong moment in the flare.