All athletes, not just figure skaters, train where they find the best conditions. Skiers where there are snow/mountains, other athletes seek a warm climate, better faciilities or whatever. And it is allowed for all of them to have "foreign" coaches at the Olympics. The world is small today and I am sure many people feel like they have two or more homelands. In the audience we often see flags that are divided to cheer for different nations/athletes.