This is another error in your thinking.
You can't solve failures in human understanding with technical solutions.
Your first instinct is going to be too try to cite counterexamples - but that only proves the point.
You're in a business that deals with people. You can't eliminate that with technology, and the fact that you think you can try is what makes you dangerous.
... have a decent crisis management or PR firm on retainer.
Which might be as much of a red flag as the initial fuckup...
On what basis do you say they have a firm on retainer?
I think many/most CEO's in this situation would make some calls to get advice on how to manage the situation -- I don't that is a red flag.
If they don't take strong, concrete steps to mitigate these kinds of problems in the future, I will have less confidence and trust in their company.