Just exactly how responsible is any executive/owner/boss/supervisor/leader for what his/her underlings/subordinates do or say? Why?

100%. That's why they make the big bucks. They take the "risk" and get the "profit".

Except if you are a CEO, then you get to resign with a large sum of money and go to your next job where you are protected from failure.

Thank you for your question and good day to you.

Many companies state up front that the employee represents the company.  

Which means they are on their own? Thank you for your reply Elyay and Happy Friday! :)