But I don’t know what drives the difference. [ between public perception of specific vs statistical results]

Most people approach such things socially rather than rationally. This is actually reasonable of them - there's no actual decision or prediction they're making based on it, so social cohesion and signalling is a fine motivation.

An important social distinction between the two types of evidence is that an individual case is directly about the person involved, with no prevarication or uncertainty if the hypothesis is accepted. If the cattle futures thing was bribery, then HC accepted bribe money. A statistical case has deniability for any individual even if the hypothesis is accepted. If the average senator buys stock on insider information, MY GUY might still be clean.

Thus, partisans who want to believe that a given individual is untainted are more motivated to deny the individual event than the statistical event. And if they do accept the event, they'll put a lot more importance on the individual than the statistical event.