Do you think the Constitution was authorizing Congress to punish violations of Vattel's book?
Note also that in the 2003 Supreme Court case saying that "the law of nations" is part of U.S. law, the phrase is not capitalized.
Doesn’t proper grammar require capitalization of explicit proper names? If so there is no disparity that you would point as examples. I too took notice of the lower case spelling in the SCOTUSA decicision. But is the argument to be that SCOTUSA did not know about the spelling as certainly capitalized in the Constitution (at least in my copy) or deliberately chose to negate the words as given in the Constitution? I think not. More likely it could be a not too well educated clerk writing the decision. Of course it is not acceptable for an ordinary citizen to believe Court justices are infallible in their thinking and writings.