I think you're missing the forest for the trees here. I was talking about democracy at a very general level in contrast to the monarchies that prevailed for thousands of years. This metahistorical generalization is bound to leave some details behind. If we focus too much on the details, though, we can miss the big picture.

Democracy is relatively unnatural, compared to monarchy or naked dominance hierarchies. Democracy stems from Greco-Roman secular humanism, whereas monarchies submit to the evolutionary law of oligarchy.

The US is a republic rather than a pure democracy, so it includes a social hierarchy (the average voters plus the political representatives). Still, the democratic aspect of the American system acts as a check on nature's influence in American society. That is, American democracy helps prevent the natural rise of tyrants in the US (since they can be voted out).

Capitalism likewise springs from progressive humanistic philosophy, and it's supposed to give everyone a relatively equal chance to get what we want. In practice, though, capitalism is all-too easily captured by the natural law of oligarchy, as it were, as we can see from the American plutocracy. This drawback has inspired a global populist backlash against neoliberalism.