But they are not. The space program is run by nasa. Thats why spaceX was a big deal. It was a private space company. The US space program is not private.
People are generally under the impression that NASA was actually making the equipment that put astronauts on the moon, for some reason.
They didn't, but they would tell manufacturers what they needed and then they'd compete to make it (in theory) and modify existing technology.
In that sense NASA is just doing what it's always done when it buys a rocket from SpaceX or whoever, the problem is the corporate expression of neoliberalism (See The Man Who Broke Capitalism) has devastated the competency of their competitors.