Its not pedantic, it's a lie meant to confuse and prime people against democracy. A republic is a form of democracy. What those that push the slogan dont tell you is that they don't want a republic either, what they really want is a theocracy or some kind of corporate dictatorship.
EDIT: This comment is heavily down voted, I would appreciate a reply as to what's wrong with it. Do people disagree that a republic is a form of democracy?