It's true though: "common modern Yoga poses", as popularly practiced in the west and in India, are derived as much from Western gymnastics as they are from classical Hatha yoga, as the GP said. I don't think that that in any way denies the diversity of yoga, or its ancient roots. It's simply a fact that traditionally, asanas were only of marginal importance and they were almost exclusively seated poses intended for meditation. There is no downward dog in the medieval texts, no Surya Namasakar, no vinyasas...

Postural yoga was popularized in India in the 1930s. Hatha yoga had been out of fashion for centuries at that point. Famous teachers like Swami Kuvalayananda, Yogendra and Krishnamacharya revived it and incorporated the standing poses from contemporary gymnastics and, for the first time, movements.

For some, maintaining a connection to the Hatha roots were more important than others. Pattabhi Jois claimed that his Ashtanga yoga (the origin of modern Mysore style in India and Power yoga in the West) was based a 5000 year old sanskrit text that Krishnamacharya had discovered, but unfortunately it was "eaten by ants".

Cultures change over time and the Silk Road is a two-way street. We all learn from each other and that is, for the most part, a good thing.