Brian Orser hit the nail on the head when she compared Yuna to Princess Di, in terms of her popularity in Korea. I think it's actually quite common for a country's people to latch onto a young, beautiful (virginal?) female personality who comes to represent all the virtues of their country in their minds. And because sports (along with movies and pop music) are some of the most widely covered events in the world these days, it's not uncommon for athletes to become these national heroine figures. I'm sure there are probably some psych/sociology articles out there on the phenomenon. I'm reminded of Cathy Freeman of Australia, Gabriela Sabatini of Argentina, and to a lesser extent Inge de Bruijn of the Netherlands and Ana Ivanovic of Serbia.
I don't think Princess Di is really the equivalent. Maybe, Orser made the comparison because of all paparazzi she attracts.
The poster above who actually lives in Korea now will probably give everyone an accurate idea of Yuna's celebrity status.