In trying some google-fu to figure out the official rules for what makes you able to compete in the Olympics for a country I ran across some interesting things.
Apparently pairs skaters in other world events, only one has to be from the country they represent. (The article also talks about some skaters that have moved around and even revoked their nationality to be able to compete Olympically.)This is also how there are sibling ice dancers competing for different countries.
The Olympics did not always have country delegations. Also, athletes have in unusual circumstances been able to compete as Independents, under the Olympic flag.
(Oh, and if you're curious, there's a link to the Olympic Charter here.)