The Nazis acted "lawfully" under their jurisdiction, but because the laws themself were unjust, it is widely recognized that they in fact did not act lawfully and so they have been trialed for it. It's called "legal positivism". The concept means, that there is in fact no difference between "law" and "moral", when it comes to war crimes. Ironically, it was the US, which established that concept.
And I absolutely agree that we can say that some countries do things that are entirely consistent with their own laws, that we will nevertheless judge to be immoral. The US is sadly no stranger to this phenomenon.
But again... what's the point? My original comment was simply addressing the legality of the situation. The US has no legal requirement to cooperate with the ICC, and has enough clout on the international stage to maintain that position. When it comes to international relations, "law" isn't the same thing as what it is between a government and its citizens. International "law" can only be enforced either through the consent of those who are party to it, or through economic or military might.
That's demonstrably incorrect, and we're talking about this exact counterexample. You're saying that the US has acted immorally (which I agree with!) while simultaneously saying the US is legally responsible, which it is not. That right there suggests that morality and law are not aligned, and that there is sometimes quite a big difference between the two.