Yours is a very US-centric view of the world. I believe we have seen share breakdowns for the US, and they are much closer.
Outside the US, none of the base assertions above are correct. The phones are not "free" (which is of course a misnomer). And in countries where consumers pay for the phones outright, Apple IS solely a luxury brand. Samsung has luxury offerings as well, but additionally competes at other price points.
Thank you for pointing this out. I think a lot of my fellow Americans wildly miss this point.