Because it's lazy short-hand for the fact that, however it works mechanically, the U.S. government is one of the people, by the people, and for the people, and the people play a fundamental role in determining their leadership through elections.
And, to be perfectly honest, people who can't see the laziness for the trees, and dogmatically assert (it's a republic, not a democracy) every time someone calls the U.S. a democracy, regardless of context, are silly angels-on-the-head-of-a-pin pedants who set themselves back every time they do it.