The Supremacy Clause of Article VI of the United States Constitution states:
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.
While federal law trumps state law, nothing under the Supremacy Clause compels a state court’s interpretation of a federal law to give way to a lower federal court. In Lockhart v. Fretwell, Justice Thomas stated in his concurrence that “a state trial court’s interpretation of federal law is no less authoritative than that of the federal court of appeals in whose circuit the trial court is located.” 506 U.S. 364, 375-76 (1993). Justice Thomas gave the following example: “An Arkansas trial court is bound by this Court’s (and by the Arkansas Supreme Court’s and Arkansas Court of Appeals’) interpretation of federal law, but if it follows the Eighth Circuit’s interpretation of federal law, it does so only because it chooses to and not because it must.”
The Supreme Court is the final interpreter of federal law. When it rules, then the states are bound.