[agensaequivocum]

They are clearly reading Federalist 10 out of context. He clearly says, among other things, there is a mean between to little representation vs to much.

> It must be confessed that in this, as in most other cases, there is a mean, on both sides of which inconveniences will be found to lie. By enlarging too much the number of electors, you render the representative too little acquainted with all their local circumstances and lesser interests; as by reducing it too much, you render him unduly attached to these, and too little fit to comprehend and pursue great and national objects.

A democracy doesn't have representation. So while his definition maybe different than what we tend to understand today, neither is he arguing that "republic" is the same as what we mean by "democracy" today.