False positives create selection bias. A polygraph detects people that are *nervous about there lies*. It won't detect the unaware and clueless, because they do not know they did anything wrong. Most people download songs to their iPhone, and assume it is legal. The polygraph not detect people that assume they are innocent. On the other hand, some people lie all of the time. A sociopath will pass the lie-detector test because they don't believe they are lying, and one person in 25 is a sociopath.
These problems have already been encountered in the preemployment screening industry. This is one of the less biased artlicles. To quote:
One recent study found faked answers for one quarter to one half of the applicants. So how can employers who want to use personality or EQ tests in their selection process mitigate against the risk of applicant faking? Counter-measures to faking include the test and retest approach to see if an individual is consistent in their answers, or asking questions that require quick responses. But counter-measures to faking may result in less reliable and valid results since some tools used to detect faking do not work well.
Bluntly, if your goal is to hire people that have done no wrong, then chances are that your hires have either lied to you, or are too clueless to realize their mistakes. Either way, it is really bad for the employer, especially if the employer is the FBI.