There are many true facts that are not important or relevant to the subject at hand. This strikes me as semantic quibbling, and slightly deceptive in that the term "democracy" is used for more than just direct democracy. That definition completely ignores the idea of a representative democracy. But I'm jot sure it really matters that much to the bigger picture which is more painstakingly accurate.
My guess would be that the downvoters believe your comment adds nothing of substance to the discussion (though it appears to be up to positive score again).
It's not a "fact" since, as your link acknowledges, it's nothing more than a pedantic and rather archaic take on the word "democracy", as if only the Ancient Greek view of the world matters. Here's a modern definition http://www.merriam-webster.com/dictionary/democracy
I've heard that before and I'm genuinely curious. Why does it matter?
A democracy is mob rule where minorities can't win unless they persuade the majority. A republic (we're a democratic republic) elects a moral governing body (congress) to make informed moral decisions. Only part f their decisions are based on the whims of the public. In theory, the rest should be based on expert witnesses from all sides of any issue (hence why people testify in congress). This allows for immoral majorities to be shut down and vice versa.