They must be counting non-government workers who work indirectly for the government. For instance all government workers are union. For instance if you work at NASA as a government employee you are unionized. AFL/CIO I believe. NASA doesn't actually DO anything anymore. They control the money and decide who gets what. Lots of graft. They fund private industries like lets say Orbital and Orbital does the actual work. They count those people as working for the government.
They do this as a matter of rule now because during Reagan they discovered government employees were actually twice as expensive as private when you consider benefits and all.
And yes, 37% administrative overhead sounds about right for the government.
Not so during the Apollo missions, making their accomplishments all the more astounding. Back then they did it for patriotic reasons and to beat the Russians to the moon as per Kennedy's dictate.