The popular founding story of the USA says the "founding fathers" set up a republic/representative democracy rather than a direct democracy because direct democracy allows the majority to oppress the minority. Therefore you need anti-democratic elements to counter-balance majoritarian power.
Were there historical stories of majoritarian oppression under direct democracies that these guys would have been drawing on? Where did the idea come from and what was it based on?
I've only seen Plato-Aristotle theorizing on the oppressive nature of democracy, and historical events where democracy was overcome by oligarchy, but I'm not aware of any stories of oppressive direct democracies running rampant.
Yes; Ancient Greek democracy was oppressive to the rich. Most societies contain more poor people than rich people, and wealthy political thinkers from Aristotle to the Founding Fathers despised democracy because its mathematics threatened the position of the rich.
The protection of the poorer masses against the in-fighting and competition for power of the leisured elite was one of the main forces behind the creation of Athenian democracy and one of the reasons why democracy was violently opposed by states where the rich kept all power to themselves, such as Sparta. In the European tradition of the ensuing 2000 years, political thinkers unanimously aligned with the elite anti-democratic elements in the Greek world, arguing that Athenian democracy was a lawless abomination in which those best suited to rule (read: those born rich) were at the mercy of the fickle mob. This is why modern democratic regimes take their inspiration more from Sparta and Rome than from Athens, and why they are not democratic in the Ancient Greek sense.
Classical Greek democracy was also oppressive to women, immigrants and enslaved people. However, all Greek political forms had these types of oppression in common, so we can't blame it on democracy as a system. The problem of majority rule exists within the body of citizens who are notionally equal, and does not describe the oppression of those who are classified as second-tier citizens or non-citizens.