Lol, just watched the vid again and AUT says core and flexibility. Time do get flexible!
DO NOT excessively train core strength and flexibility because of this video. They don't HELP your vert, they can only HURT it, if not developed to a certain degree. If you have enough flexibility and core strength to do a MAX effort jump while keeping your spine/pelvis stable (which isn't that much), any more core and flexibility training will not = inches on your vert.
AUT: "Leave them legs alone" NO.
I know what you're thinking, he's AUT! higher vert than anyone on here. He's genetically gifted with those hops, he did not get those hops from AB training and stretching. Sorry but he does not know what he's talking about. But can you blame him, he's born with a ridiculous vert, and a dumb coach told him it's all abs and of course he'll believe it.