Final answer:
The Supreme Court in United States v. Nixon ruled against Nixon's use of executive privilege to withhold the Watergate tapes, leading to their release and contributing to his resignation.
Step-by-step explanation:
In the case of United States v. Nixon, the Supreme Court did not rule that Archibald Cox had overstepped his bounds; rather, it ruled against President Richard Nixon's use of executive privilege to withhold the Watergate tapes. The Supreme Court's decision was that executive privilege could not be used to withhold evidence relevant to the investigation of the Watergate scandal. Ultimately, this led to Nixon having to release the tapes, which played a significant role in his eventual resignation from the presidency.