Most of the time government hires (and has for a long time) the traditional defense contractors or government-specialized small contractors to do their IT work. It is actually mildly impressive that a 'normal business' IT provider like AWS has broken into the government field.
Often these contractors, with experience in getting and administering federal contractors, will hire other contractors to do some of the other work. It's quite possible that's what's happened here.
See http://www.lockheedmartin.com/isgs/