According to the source, more democracy makes these people less reassured, not more. The United States just happens to be one of the most democratic countries in history, wherein even Sheriffs are elected.

A large part of the problem is that America actually has too much democracy for the tastes of a third of its population. Consider there are three separate branches of government purposely set in permanent opposition to one another. The U.S., of course, also has many levels of government, with voters passing judgment on all, from the president right down to the school board and dog catcher. Thus, there are constant demands for electoral participation and endless exposure to political debate, dispute, and conflict. This is indeed a vibrant democracy, but you have to understand it is simultaneously, for the same reasons, anathema to authoritarians.