You have a point but let me make a counter -- it's the subordinate who must prove their trustworthiness to the superior. Which in your view, seems to be the people and their government, respectively.
If you had said, "The government acts in a trustworthy manner, and the people, in turn, trust their government", then our viewpoints would be in alignment.
If you had said, "The government acts in a trustworthy manner, and the people, in turn, trust their government", then our viewpoints would be in alignment.