That the Constitution defines it as such is simply a matter of documentation of a purpose. You have to actually internalize a purpose and values system for it to be useful and “real” in the sense that it drives what you do as an organization. This seems a more proper distinction that feels accurate to me in making the author’s point but that is itself a hard point to falsify.
The other way to think about how to steel man the idea would be to think about how the government measures its success which is most likely by whether or not those in power keep staying in power? The bureaucrats who are subordinate to the government have much less (any?) stake in that measure so again it would be tough to think about purpose there.