Who's privacy? You mean the person paid by US Taxpayers dollars? This is not their medical records or history of beating their wife. This person was on the US Taxpayer's payroll at the time.
Screw the people is the governments motto.
That means the FAA guy is lieing through his teeth. Time to get Congress on his case and find out who the people were on the tape, who the so-called "quality assurance" guy was, and then demand to know their current salary!