That's a shift in goalposts from the original post's claim of "common modern Yoga poses" - Yoga practise in the west is only a small portion of modern Yoga in general. There's a difference between saying "common modern English borrows a lot from Hindi grammar" and "modern English spoken in India borrows a lot from Hindi grammar" - and there's as much difference between your statement and the statement the original comment made.
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.
And Yoga went from an obscure practice of (mostly male) Indian ascetics to a household name the world over (practiced a lot by female lay persons).
I find it a great story, though my initial comment on this thread was down voted. We like marketing here on HN right? This is marketing.