I don't agree that domestic law always wins. It all depends on the situation.
If a country's domestic law violates international law, the extent to which that country gets away with it depends a lot on how powerful that country is. Great powers have much more ability to violate international law with impunity than small countries do.
And in this particular case, it is not that US law and international law are actually in conflict. It is just they assign different meanings to the same words. Even the US government generally accepts the internationally standard meanings in international fora.
If a country's domestic law violates international law, the extent to which that country gets away with it depends a lot on how powerful that country is. Great powers have much more ability to violate international law with impunity than small countries do.
And in this particular case, it is not that US law and international law are actually in conflict. It is just they assign different meanings to the same words. Even the US government generally accepts the internationally standard meanings in international fora.