This is more propaganda than reality, though. Most democratic societies today have evolved out of very non-democratic ones gradually, in a process where the elite had given up
some of its privileges to prevent losing all. One of the tricks involved in that process was the notion of a "popular mandate" - not that this isn't a thing, but genuine cases of it are far less common than politicians using the fact that more people voted for them as some kind of argument in support for some specific policy of theirs.
In practice the difference between a democratic and a non-democratic society is more quantitative. In a non-democratic society, people still have a check on the government - they can revolt, and, being far more numerous than any security apparatus that can be maintained over a long time, the rulers therefore cannot simultaneously piss off too many people at the same time. So the bar is pretty high, but not entirely insurmountable. In a democratic society, the people also get an option of protest voting, which provides a safety valve that bleeds off a lot of effort that would have otherwise gone into potential violence, but at the price of making this kind of "voter revolt" less costly to participants and thus more likely. However, representative democracy is still pretty bad at accurately reflecting population preferences - it still takes a lot of abuse before protest voting becomes prevalent enough to alter election results. And then, of course, new mechanisms were developed to "manage" democracy - more efficient propaganda, mostly.
Thus, in practice, governments can indeed be treated mostly similarly to other organizations in this regard.
