Video sucks. Total oversimplification.
They completely missed my favorite story, which was that the bidding between Shenyang and Chengdu for the fighter project was rigged for Shenyang and Song was just supposed to put on a little show to make it look like there was competition. But he decided that any chance was a chance worth his 100% so Song put on a passionate presentation of the J-10 design that was so overwhelmingly superior to Shenyang's proposal that even those who were corrupt and bought out were swayed to vote in his favor. Thus, the J-10 program was born.
My second most favorite story in the J-10 creation saga was when J-10 test pilot Li Gang said that the aircraft he was sitting in represented the hope of the nation and is like a child of everyone who gave all their dedication and time to create, so as long as the prototype did not disintegrate in the air during test flight, he would not eject no matter what, putting his own life down for any minute chance to save it if it lost control. His words can bring tears to my eyes every time I recall them. They missed that part too.