In the United States v. Apfelbaum case of 1979, the Supreme Court ruled that a witness who testifies under a grant of immunity can be prosecuted for perjury if they lie during their testimony. The defendant, Martin Apfelbaum, was subpoenaed to testify before a grand jury and given immunity from prosecution based on his testimony. However, he made false statements during this process which led to him being charged with perjury. He argued that these charges were in violation of his Fifth Amendment rights against self-incrimination as well as the statute granting him immunity (18 U.S.C §6002). The Supreme Court disagreed with Apfelbaum's argument stating that while an individual granted immunity cannot be prosecuted based on their truthful testimonies, it does not protect them from prosecution for committing perjury or making false statements during such proceedings.

In the dissenting opinion for United States v. Apfelbaum, Justice Brennan argued that the majority's decision to allow a witness's false statements made during an immunity hearing to be used against him in a subsequent perjury trial was inconsistent with the Fifth Amendment protection against self-incincrimination. He contended that this ruling would discourage witnesses from testifying freely and honestly at immunity hearings due to fear of potential prosecution based on their testimony. Furthermore, he believed it could lead prosecutors to use immunity proceedings as traps for unwary witnesses by encouraging them into making potentially incriminating statements which could later be used against them in court. In his view, such practices were not only unfair but also undermined the integrity of judicial proceedings and violated constitutional principles.