Update....”Indian Style” was NOT referencing Native Americans and was in fact referencing actual Indian people, and more directly the lotus pose in yoga. The Polish call it “siedzieć po turecku” (Sitting Turkish) for this same reason. https://twitter.com/_hannahbanana14/status/1283253690657275904

My question, however, still stands. Did Europeans not know how to sit this way until they went to India and saw people practicing yoga? How were they sitting before?

Also throughout my research (in-depth Googling) it does seem that for some reason Americans did perceive the original name as a reference indigenous people even though that wasn’t the origin—so much so that many of us discontinued use of the phrase several years ago

Another source contradicts this and says:

when colonizers came to America from Europe, they actually had never needed to sit on the ground before. They had exclusively sat in chairs. So they saw the Indigenous tribes sitting on the ground in this style and nicknamed it such.

Yet a third Internet Human claims the phrase was not popularized until later when TV shows began portraying “Cowboys vs. Indians” storylines. The shows fictionalized and generalized the colonization of the American West. Before this, it was called Tailor-style.