This portion of the ad Herrenium (a rhetorical handbook and one of our early substantial Latin prose works, pre dating the Ciceronian corpus) is often quoted in books about Memory. Not so much by historians of the republic. One of the most read authors on Memory, Yates, speculates that the scene may have been witnessed by the author either in real life or on the stage.
I’m of the opinion that this would be a very poor teaching example if both the verse and the imagery were not likely to be familiar to the intended audience. This is not about the author’s personal experience, but about how oratorical preparation should be done. Elsewhere, the author certainly picks known images.
I suspect the story come from the narration of how plebeians or Romans more generally in some specific context won the right not to be flogged. This right was a very slow evolution over centuries and an extension of the rights of provocatio and made on the analogy to protections from summary execution. Oakley gives a good concise summary of the evidence:
Here’s the coin (RRC 301/1) under discussion:
As an aside Brennan thinks the Marcii Reges were patrician (p. 901):
This translation of a fragment of a Cato’s against Thermus’s Triumph is from an essay by Sciarrino (p.58):
This is a translation of the only surviving fragment from Cato’s speech on King Attalus and the tributes of Asia (Image links to source):