[sourcery]

If they were referring to Vatel’s book then wouldn’t they have capitalized “Law of Nations”?

They did. From Article I, section 8: "To define and punish Piracies and Felonies committed on the high Seas, and Offences against the Law of Nations;"

[Non-Sequitur]

They did. From Article I, section 8: "To define and punish Piracies and Felonies committed on the high Seas, and Offences against the Law of Nations;"

They didn't in the Supreme Court decision.