If you think there’s no problem with suiting up against your own country, then I don’t know what to say.
She didn’t suit up against her country, it’s JUST sports. Nothing happens if “our” team wins or loses, there’s no effect on the world. It’s a game. You’re trying to make it sound like she took place in armed combat against American troops, THAT would be suiting up against her country, but that’s not what happened.
Again, be consistent. If you’re going to say it’s just a chunk of metal admit it’s just sport. If you’re going to insist sports matter, then the medal matters. You can have it either way, but you can’t have it both ways.