Over the years, I have encountered people who like to split hairs on democracy vs. republic. I never really understand why, but maybe you have something here: to make democracy sound bad.
I like to point out that, legally speaking, Canada is a still a monarchy. The Queen of England can veto any law created by Canadian Parliament. But Canada very much behaves like Plato's republic--even if we prefer the term "democracy." The Royal Family has stayed out of legislation building for several centuries--and shows no sign of wanting that job.
Democracy is a term that has become quite broad in meaning. We shouldn't assume the Athenian democracy applies to all usages of democracy.
Sort of like socialist, which is often defined as someone who wants to put all business and commerce into the hands of government.