Well, he speaks only about Yang style, not Taijiquan in general.
However, notice that he is arguing about who started Yang
FAMILY Taijiquan = Yang shi 氏 Taijiquan. 氏 means clan, family, lineage and is often what we translate to "style".
But here's the rub. "Yang Family Tai Chi" is a registered brand. It's a brand created by Yang Jun himself and his father Yang Zhenduo. This is their own standardized Tai Chi from what Yang Chengfu taught as his "new style", something created for the masses to keep health.
So when he speaks about Yang family Tai Chi, I find it a bit deceptive. He actually answers to his own students about the art that they practice. So when Yang Jun speaks, it sounds as that the simplified Yang version that they do and teach, was created by Yang Luchan.
This is a bit like the Chen stylists claim that Chen style is the oldest Taijiquan and use Chen Xiaowang's modern standardization for something much, much older and probably much different.
Yang Jun has good marketing and branding skills, no doubt about that.