I’ll have to disagree with you here. If a person is working for an organization, they represent that organization, whether they like it or not. If someone receives good customer service from an employee, they’re quick to give good reviews and recommend the company to others, so why not the other way around?
In light of recent negative events occurring at United, it was their responsibility to be proactive and give their employees, especially the frontline ones, who directly serve the customers, a heads up on how to prevent or handle such crisis in the future, which they failed to effectively do. Besides, they did accept full responsibility for the incident.
If investigations do find the flight attendant responsibile for the death of the dog, she should be held accountable and local laws should fully be applied, even if it means jail time.