If you’re going to devalue the Olympic medal as just “a piece of medal” then you should be honest and devalue the whole even as just sport. Countries don’t really win or lose anything in international sports, it really just effect their uniforms and available teammates. One didn’t want her, another she was eligible for did, so she went the team that wanted her and won.
If you think there’s no problem with suiting up against your own country, then I don’t know what to say.