The government has multiple branches... They're the legislative branch.
If we're going by your logic, the executive branch is the one that is not part of the government because they don't get to decide how to govern.
https://www.whitehouse.gov/about-the-white-house/our-governm...
https://www.usa.gov/branches-of-government
https://people.howstuffworks.com/three-branches-government.h...
> All but a few are millionaires who make more income from non-government sources than that paycheck. By virtue of their office, they're also well connecte
All of this is true for the executive branch too.