As a useful term, "democracy" has to refer to any political system in which the citizens formally possess equal rights and exercise an equal voice in the selection of the government officials. The distinction between and oligarchy and a democracy is purely a quantitative one, hence open to fluctuations in standards. Thus, Athenian democracy or US democracy prior to the Sixties can be argued not to be democratic. In practice, a universalizing moralistic discourse is not as useful for clarity as historical context. So, yes, slaver America was a democracy. It's just that "democracy" is just not what it's cracked up to be. The attempt to redefine the term as an effort to annex a particular vision may have good motives, but it's still confusionism.
A democratic political system can be devised to favor forms of property. If you try to redefine "democracy" as one which favors abstract individuals defined by their equal rights, such systems are not democratic. The difficulty with this definition is that such a classless government has never yet been devised. It even has only been aspired to as a goal by anarchists and communists.
Indeed, historically, "democracy" has largely meant such a property characterized government. And a government that uses democractic majorities to tamper with property are ipso facto condemned as tryannical. This is official US government interpretation, the grounds on which the late Hugo Chavez was labeled a dictator, despite having repeatedly won majorities in perfectly acceptable democratic elections. It was similar figures in ancient Greek and recent Italian city states that inspired much conservative condemnation of "democracy" as inevitably leading to the lower orders misusing the government to revise property.
Thus, it is entirely possible to devise a democratic government with formal equality between citizens and equal suffrage amongst them combined with a commtiment to defense of certain kinds of property. The statement that the US is a republic refers to this kind of arrangement. Only by the anarchist notion of equal individual rights is this undemocratic per se. Formally, the US constitution allows that the arrangements to defend property of a certain kind can be changed, as in the Thirteenth Amendment. Thus the observation that the US is a republic does not forbid drastic social and political reforms.
However, in practice, every single person who intones that the US is a republic, not a democracy, does so in a context that makes it perfectly clear that they do not believe that property relations are ever to be the subject of democratic politics. All these people adhere to the slaver interpretations of the constitution. Whether they are so desperate to argue for an property system that remains inviolate regardless of how many people suffer from it is rooted in racist love of slavery, or whether they fear and hate socialist policies, again is irrelevant. The logic, and its immorality, are the same.
Quotations from the "Founding Fathers" are the province of political conservatives who want to pretend the US constitution is at least quasi-divine. (Lots argue amongst themselves it really is divine.) But if you read contemporary writings you'll find the people of the time very much thought of themselves as setting up an empire.
It seems many thought of America as the British Empire new and improved, continental instead of insular. They may have seen their projected Empire as better than the Spanish and Portuguese despotism in the rest of the western hemisphere. The simple truth is that "empire" was not negatively viewed as a necessary violation of another people's equal rights by any but the most radical Enilightenment thinkers.
Lastly, the very popularity of "republic" stemmed very much from the example of the Roman Empire, which existed long before the alleged "democratic" tyranny of Julius Caesar, the popularis who rode roughshod over the property of the Roman boni, the "good people" who owned property. The fact the the empire really began under Augustus, who was equally a Claudian, i.e., one of the greatest of the patrician families, was too obvious to see, I suppose.