This is sound advice. You have a significant amount of control over people's lives as a manager, and that should be treated with a level of respect. You have no idea how people feel, and it is quite possible that someone you manage doesn't know where they stand with you. At times that is more than enough to cause them stress and even convince them to look elsewhere. Work is stressful enough, and you don't need to add…
Higher level performers tend to disproportionately believe then need to improve so they tend to take group jokes or threats of termination much more seriously than underperformers.
Be very very careful making groups statements and jokes about performance and firings. It’s a fast track to losing high performers who leave because they start to believe they are not wanted and not doing a good job.