I always thought that the great lie in the employment statistics was due to high percentage of the American population that is in jail. USA has the greatest number of prisoners of the developed countries, and it skews the statistics.
It cannot be a very great lie, because the incarceration rate is <1 %, and unemployment is generally an order of magnitude larger. And: incarceration rate includes also people who are not in in the potential workforce (i.e. are not working age).