In Killian v. United States (1961), the Supreme Court ruled on a case involving false statements made under oath. The defendant, Mr. Killian, had been convicted of perjury for falsely testifying that he did not receive certain payments in connection with his official duties as an officer of a labor union. He appealed to the Supreme Court arguing that his conviction was invalid because it was based on circumstantial evidence and lacked direct proof of falsity. The court disagreed with Killian's argument and upheld his conviction stating that perjury can be proven by circumstantial evidence alone if it is strong enough to establish guilt beyond reasonable doubt. The court also clarified that while corroboration is required in some jurisdictions for certain crimes like treason or sedition, there is no such requirement at federal level for perjury cases. Furthermore, the court rejected another argument put forth by Killian which suggested that since he believed the payments were loans rather than income related to his union position; therefore he didn't knowingly lie under oath about them - hence should not be guilty of perjury. This ruling reinforced two important legal principles: firstly, circumstantial evidence can suffice in proving guilt beyond reasonable doubt; secondly, belief or perception does not excuse one from making false statements under oath.

In the dissenting opinion for Killian v. United States, Justice Hugo Black argued that the majority's decision to uphold Killian's conviction was a violation of his Fifth Amendment rights. He contended that by allowing an FBI agent to testify about statements made by another person who had not been called as a witness and could not be cross-examined, the Court was denying Killian his right to confront witnesses against him. Furthermore, he disagreed with the majority’s interpretation of hearsay rules and believed they were too broadly applied in this case. Justice Black also expressed concern over potential abuses of power if law enforcement officers are allowed to present uncorroborated testimonies from absent witnesses without any opportunity for cross-examination or rebuttal.