Defiant is absolutely correct and your response shows complete ignorance of the Constitution and the powers and jurisdiction of the SCOTUS.
Art. III, §2 gives the Supreme Court original jurisdiction over certain types of cases, including cases in which a State is one of the parties. There is a significant difference, however, between "original" jurisdiction and "exclusive" jurisdiction: Art. III, §1 gives Congress the power to create "inferior courts" (i.e., district courts), and in doing so, Congress has given jurisdiction to the inferior courts that overlaps the original jurisdiction of the Supreme Court, including jurisdiction to hear cases in which a State is one of the parties.
In addition, under the Separation of Powers doctrine, the Supreme Court, since its earliest days, has interpreted the original jurisdiction clause to mean concurrent jurisdiction, as opposed to exclusive jurisdiction, with the jurisdiction of the inferior courts that Congress has created. Indeed, by its own rules -- again, under the Separation of Powers Doctrine -- the Supreme Court has limited its original jurisdiction, with few exceptions, to appellate jurisdiction from the inferior courts that Congress has created under Article III. (One of the exceptions is that the SCOTUS has retained original jurisdiction over cases between two states that involve territorial boundaries.) Thus, the Supreme Court could have exercised original jurisdiction, over the Arizona Immigration Case, it has by rule and precedent chosen to to defer to the the concurrent jurisdiction of the District Courts.
Lastly, before you blame "law school revisionism" and liberal activist judges for overriding and perverting the Constitution, please note that the Supreme Court precedent and rulemaking authority to limit the exercise of the Court's original jurisdiction, goes back to the days of Chief Justice John Jay (one of the authors of the Federalist Papers) and Chief Justice John Marshall, at a time when the Justices on the Supreme Court who made the rules and precedent to limit original jurisdiction, were the Founding Fathers of our great nation.
Thanks, Labyrinthos, you said it all so I don’t have to.