Social dynamics comments:
Trying to set the record straight is perceived as high effort – especially when you give quotes, details, analysis, etc.
Setting the record wrong was low effort.
Asking audiences to change their minds and believe the right thing is seen as needy. You are going to them and wanting them to do something.
Setting the record wrong is not seen as going to the audiences and asking for something.
Putting people in a position where they need to set the record straight is a social (and logical) attack that’s very hard to counter. Clarifying the issue in response, even for audience members who read the clarification, doesn’t work well. People don’t like it. In general, they intuitively see it as weak, tryhard and other bad things.
Turning it around and criticizing the person who harmed your reputation is problematic too. If he attacked you indirectly, and you then criticize him directly, you will be seen as the aggressor. Many audience members will believe him if he claims he was merely sloppy, and think you overreacted, and will see you as reactive to minor wording details which makes you seem super reactive (low status) b/c who cares about minor wording details? High status people are only triggered by big things, not little things. They are stable and safe enough not to worry about little things. And he doesn’t even have to admit he was wrong. And the more effort you put into showing he’s wrong, the socially worse you look if he then casually pretends it was practically a typo. But if you put in less effort, then it’s easier for him to deny he was even wrong since you haven’t laid out a bunch of clear, comprehensive arguments.
People put a lot of work into figuring out what small errors they can make that will be perceived as low effort or not doing much, but which will be threatening or damaging to others in big ways. People put lots of behind-the-scenes effort into finding misdeeds they can do that will do damage disproportionate to the apparent effort level, so they can make others look over-reactive.
EDIT: Forgot one of the points I was gonna say: Most audience members are sloppy thinkers themselves so they feel kinda threatened if you criticize sloppy writing/reading just like they routinely do, and they sympathize more with the person who made a mistake that they can totally see themselves making (either intentionally to be mean or unintentionally due to incompetence – they are capable of both). People will also like deny the misframing or misreading is an error, but then say that, in the alternative, even if it was an error, it’d be a reasonable and understandable one (but they use less clear wording than this).