The choice of words to Benjamin Franklin was deliberate -- the citizen asked whether we would establish a Republic OR a Monarchy, because THOSE are separate, competing forms of government. She did NOT ask if we were "a Republic or a Democracy", since they co-exist in most nations.
The founders established a constitutional Republic with free democratic elections. Thus, the United States is representative (indirect) democracy where WE THE PEOPLE are the ultimate source of authority and choose our representation in government thur free democratic elections.
If they had meant for "the Republic to NOT have democracy", they would have established a Cuban-style dictatorship where power is derived from the state instead of the just consent of the citizens.
End of story.
BM for later