Let me be more succinct in my comparison ... elements of Hatha Yoga are practiced in many nations worldwide today. And yes, that even includes Joseph Pilate's workout as his original source material was Hatha Yoga, along with some western physical culture.
With that said, most of these practitioners are not considered Hindus (and/or overseas Indians), even though some elements deriving from Hinduism are in their daily lives.
And thus, one can't say that the nationalistic/spiritual torchbearers of Zoroaster, a.k.a Cyrus the Great and all the emperors (before the Caliphate) which succeeded him, are of Indian origin due to Zo's education of Vedic scrolls.
And yes, in the west, Pilates is considered one of the best conditioning programs out there. So I guess it's time to hand Joe an Indian passport for all of his efforts in getting yoga into the hands of countless nations. FYI, I use a lot of Pilates and yes, it's great for toning, balance, and building core strength.
www.youtube.com/embed/sbd4qiPLWOQ