In Canada, medallists (excluding the hockey teams which I didn't check) were all born in Canada, but Jan Hudek, which was born in Czech Republic (or more exactly, Czechoslovakia).
Patrick Chan has Hong Kong parents, but he is born in Canada.
In sports, people rarely deflect to Canada. It's usually the reverse (Begg-Smith to Australia...)
We had a Jamaican on the bobsled team in 2010 I think.
The Russians really set out to purge other countries of their athletes. They tried to get some curlers from Canada (Jason Gunnlaugon's rink), but that failed when the team didn't want to give up their Canadian citizenship.