There is not only the 2008 opinion.
From 2006 there is also Sanchez-Llamas v. Oregon 548 U.S.331
From the syllabus:
In contrast,Article 36 has nothing to do with searches or interrogations and, indeed, does not guarantee defendants any assistance at all. It secures for foreign nationals only the right to have their consulate informed of their arrest or detention—not to have their consulate intervene, or to have police cease their investigation pending any such notice or intervention. Moreover, the failure to inform a defendant of his Article 36 rights is unlikely, with any frequency, to produce unreliable confessions, see Watkins v. Sowders,449 U. S. 341 , or to give the police any practical advantage in obtaining incriminating evidence, see Elkins v. United States,364 U. S. 206 .
And Article III Section 2
The judicial Power shall extend to all Cases, in Law and Equity, arising under this Constitution, the Laws of the United States, and Treaties made, or which shall be made, under their Authority;--to all Cases affecting Ambassadors, other public Ministers and Consuls;--to all Cases of admiralty and maritime Jurisdiction;--to Controversies to which the United States shall be a Party;--to Controversies between two or more States;--between a State and Citizens of another State;10 --between Citizens of different States, --between Citizens of the same State claiming Lands under Grants of different States, and between a State, or the Citizens thereof, and foreign States, Citizens or Subjects.