Anybody can give a course to anyone and teach anything they want as long as they don't claim to have credentials they don't have and as long as they don't claim that taking the course provides benefits that it does not. For example, I could set up shop teaching personal defense courses, and as long as I didn't claim to be a certified instructor and didn't claim that graduating from the course gave the student special privileges then no one could tell me what to teach.
If they're CERTIFIED instructors, then they must abide by the guidelines set forth by the certifying entity, and if they're teaching a course that provides a special benefit or right (like a CCW course) then they must abide by the government guidelines regulating the course.
In your case, since you're teaching a specific government defined course, you must abide by the guidelines set forth by the government when teaching the course.
I don't know about the laws everywhere, but at least some states do not require specific instruction courses to be taken by CCW applicants. Nevertheless, some instructors teach CCW courses to provide additional information to CCW hopefuls. I believe that WA is this way. Since the government doesn't require a course, the probably don't specify what the course must say, and therefore the instructor has pretty wide latitude in what he teaches. Of course, to one extent or another, he is liable for what he teaches if it turns out to be dangerous or illegal.
In TX, the CHL courses are rigidly defined, but the instructor doesn't need to be LE. The instructors are trained by LE (TX Department of Public Safety) but they themselves carry no LE credentials. The CHL course does include portions with deal with the legal aspects of the use of deadly force and carrying a handgun.