Don's points are very good. I mean I could say I worked with the Military (* one or two guys who retired or were reserve or even on leave worked out with me *), I could say I worked and taught local police, (* one or two sheriffs with an EMT or two trained for a while as well as other departments *), I could say I have taught at a University and should be called a Professor (* Self-defense class taught intramural *) or many other things to make it sound better than the truth is.
Yet, I find it so much easier to just remember the truth, and as this is what I remembered and others have seen and witnessed as well it is easier to verify or deal with, be it good or bad or indifferent for me.
You just hit on one of my pet peeves...
If you're going to say you trained military or law enforcement personel, fine. But be honest about the way you trained them; they came to your class, and took part as students, or they attended a seminar you taught once. Don't try to imply that your a police instructor because a cop took part in your class for families. Don't say that because a Navy SEAL or two joined your MMA club for a month or, on their own time and dime, brought you in to show your fancy knife techniques, that you "TRAINED THE NAVY SEALS!" Be honest; say you taught a seminar to a group of SEALs or whatever.
There are martial artists out there who legitimately train and instruct police; in my area, Maurice Allen, an internationally known Judoka, is one. He really does teach classes at several police academies in the area. I'm not, even though I am a police officer and field training instructor (but not defensive tactics instructor), and I've had other law enforcement officers as students. There's a lengthy list of people who contributed to the development of the USMC Martial Art program; they can make that claim. I can't, even though I've taught Marines.
And I hate it when people try to boost their credentials that way... Especially since some of them have plenty of legitimate credentials to claim! You can usually tell the ones who don't pretty quick...
As to titles... Well, some people say that I'm entitled to be called "master." I don't know; I called my instructor by his first name. I still do. I don't expect my students to kowtow to me or address me by silly names. Their conduct shows whether they respect me or not. If the tradition of an art uses the title "professor", that's fine. I consider it similar to an academic doctor versus a medical doctor here in the US; outside of the classroom/academic world, few academic doctors (PhDs) push to be called "Doctor." We generally reserve that for medical doctors here.