Let's review, shall we?
This Constitution, and the laws of the United States which shall be made in pursuance thereof; and all treaties made, or which shall be made, under the authority of the United States, shall be the supreme law of the land; and the judges in every state shall be bound thereby, anything in the Constitution or laws of any State to the contrary notwithstanding.
The International Court of Justice is the primary judicial branch of the United Nations. The United Nations was formed via treaty in 1945, and the United States is a signer on that treaty. The United States is subject to the International Court of Justice. Period. I don't give a ripping damn what the Roberts' Court says. But here's the trick, and why Roberts, and Bush incidentally, is such a complete and total idiot: The ICJ is for nations to sue other nations about international issues, and is not the correct court that should be drawn upon for the Texas death-row inmates.
Rapists and murderers who cross national borders should be tried under the laws of the International Criminal Court, a DIFFERENT JUDICIAL AGENCY outside of the ICJ and part of a separate treaty. This treaty says that individuals who commit crimes should be held accountable for those crimes. So why can't the Mexican citizens be made subject to this court and tried properly? Because the ICC applies in both directions, and the United States Federal Government is too CHICKEN SHIT to sign the treaty, thinking that US Citizens who break laws and rape and pillage and murder should not be subject to the same laws that they are now trying to apply to the citizens of other countries.