Who cares? I ask the question as a lawyer, who always responds to "Is X a Y?" with "for purposes of what?" What decision hangs on the answer to the question? What will anyone do differently if they come out on one side or another?

International law is and should be taught in law school. (I took it, and it's where I learned the "Act of State" doctrine, which, basically says that International Law isn't "law" for some purposes.)

Courts resolve international cases all the time. Most do so as an application of domestic law to international events. Is that "International Law"? Some say yes, some say no. But neither answer changes the outcomes of the cases.