You are indeed missing something. If not for the individualism of the astronauts, they would never have gotten to the position where they were capable and suited to become astronauts. It wasn't the government who made them enter flight school n their youth or struggle and achieve all of their goals up to and including the Apollo program.
Both were premier examples of American exceptionalism -- but it was the Astronauts who were mentioned as prime examples of self-reliance in the sentence being cited.
For a prime example of the ground team plus the resourceful individuals in space forming a "whole greater than the sum of the parts", there is no better example than the survival of the Apollo 13 crew...