It is very true that the ranks of private security and government security are heavily populated with former law enforcement officers, or those moonlighting in security positions as security officers and not commissioned officers. When you compare uniforms the security personnel may look very similar to local law enforcement officers. If it is an armed security force they will carry weapons and other law enforcement "tools of the trade."
As the story above relates, it is important to remember what role you are playing. Perhaps 20-30 years of experience kicks in and you fall back on behaviors that you used in the past--but are inappropriate for a private security force.
While you can teach classes on this it is the muscle memory and way of doing things as you have always done them that can take over in a situation. While some of this would be good, such as in a fight to subdue as suspect who is intending to do you or others harm, there are other situations that need to be thought through carefully before taking action.
