"Reputation is just a question of outside perception of a nation. It has nothing to do with what the nation is actually doing."
Agree entirely, except that such reputation is not only a questino of perception of that nation from the outside, but also from within.
As a general rule, the 'facts' presented by the fact-providing source are irrelevant if the legitimacy of the fact-providing source is in question.
In this case, the source for the 'facts' about what the US is actually doing in the world (and in its own country) is monopolized, for the source is the US government itself - an inherent conflict of interest that results in tyranny.
The facts which would portray what the US is doing exactly is typically classified / kept secret from the public by the US government. Naturally, then, there is going to be a low perception of the legitimacy of the US government as the source of the few facts that are declassified, or released, leaked to / uncovered by the press, for it is perfectly plain to see by the very prevalence of there being secret or classified 'facts' to begin with that of course the public is not going to be fully informed as to what the US is actually doing. There is no way for the public, then, to determine whether or not the US is in fact doing as it claims, in this case 'promoting democracy / democratic values in a morally responsible manner.
The recourse, for an inquisitive public concerned with whether or not the US is in fact promoting democratic values / democracy responsibly is to compile facts from the little information that is available to them and do so in light of the actual prevalence of democratic values / democracy at home and abroad, filtered by their personal, subjective experiences of democratic values / democracy in their own lives.
The issue is that clearly a growing number of people's evidential experiences of democratic values / democracy reveals the contrary as to what the US government claims. They perceive a police state, corruption, elitism, the promotion of anti-democratic values, the degradation of the rule of law as it might suit military and / or economic interests of an increasingly global, unaffiliated elite, and a general lack of a humanitarian ethos, etc..
There comes a point, often suddenly and without warning, catching the 'fact'-providing governing authority unawares, when the public at home and abroad simply ceases to recognize the legitimacy of their governing authority.
For most governments in the world, such is happening as we speak: the general public of the entire world does not place much credence in the stated purposes or claims made by governments as such might be presented by government-sponsored leaks to the mass-media.
Plainly put, its no secret anymore that what governments are actually doing is secret and in many cases irresponsible, anti0thetical to democratic values, evidenced by people's subjective experiences to that effect. It is generally understood that any facts released in an attempt to portray governments in better light in this regard is propaganda. People understand they are not going to be adequately informed to the extent that they could possibly be responsible voters, and, as such, there is a growing sense of the illegitimacy of the entire system.
The social consciousness of the world's people as a whole can be characterized, I think, as deeply embittered resignation to the tyranny inherent to very design of what is clearly an illegitimate system.