i think this is what they're referring to (in employment law it is commonly referred to as 'a garrity situation' - but you'll frequently here it is a 'garrity act' because the law established there holds):
Garrity v. New Jersey, 385 US 493 (1967). Under Garrity, a government employee cannot be faced with the choice between self-incrimination and termination. If the employee is coerced to speak under threat of termination, the statements cannot be used against him in a subsequent prosecution. According to an FCC source, employees faced with an investigation should be given a "Garrity Warning," in which "The individual is apprised of his or her right to remain silent if the answers may tend to incriminate him or her; that anything said may be used against him or her in either a criminal or administrative proceeding; and he or she cannot be disciplined for remaining silent. " So, in a Garrity situation, the employer gives up their right to discipline the employee for their silence, but retains the right to prosecute the employee for anything they might say. Thus, Garrity is said to cover "voluntary statements."

toward the end, this Newshounds video states, "legally, it looks like any immunity agreement given under the Garrity Act is null and void ..." -- while there is no such Act of Congress, there is a Supreme court decision (Garrity v. New Jersey) of similar name.