Indeed, the FBI participated in the criminal investigation of the late Doug Williams, who offered training on how to pass or beat a polygraph "test." Because there was no actual crime for which to prosecute him, federal agents set out to stage one in a "sting" operation they dubbed "Operation Lie Busters":
You are correct. The Employee Polygraph Protection Act of 1988, which otherwise prohibits the use of putative lie detectors by employees, provides exemptions for such cases.