Dear RTFM:
With regard to informing someone that you have a gun, the idea is to train yourself to do the right thing to justify your actions legally. With that said, please understand that I am not an attorney (I have to much self-respect for that), so I am speaking logically, not dispensing hard-and-fast legal advice.
Here's my logic:
According to our legal system, I'm supposed to be judged by a jury of my peers. So, if I was on trial for shooting a home invader, I would expect MY peers to show up wearing NRA hats and reading SWAT magazine, right? Well, that's not gonna happen. Instead, I'll have a bunch of nice little old ladies who hate violence, love cats, and can't understand why I didn't just put the perp in a wristlock until he found religion. As such, my job is to get them to understand that I was in fear for my life or was defending my family against the threat of death or greivous bodily injury and that my actions were reasonable and justified.
If you have called 911 or if there is anyone who could serve as a witness for your actions, I believe that clearly stating
"You are in my house. Get out"
"I have called the police."
"I have a gun."
are all good ideas. That way, the home invader knows that he hasn't somehow kicked in his OWN front door to threaten his OWN family, the police are aware of the situation and are en route, and you are prepared to defend yourself. If, after all that, he still chooses to press an attack, his intent--and your ability to justify and articulate that you were in fear for your life--are pretty clear.
Some folks may feel that this is unnecessary and that once he's in your house, it's "game on." If you live in a state with a castle doctrine, that attitude is more appropriate. However, if you live in Massachusetts or California, memorizing those phrases might not be such a bad idea. Please remember that to ensure that TBD has a broad relevance to our viewers, we really try to cover all the bases thoroughly in the time we have available (which, by the way, is actually 19 minutes per episode). If something we say or show doesn't apply to your exact circumstances, that's OK. If showing that item motivated you to consider your specific situation and either forumulate or revise your plan, it's still a success. And as a student of personal defense, that's how you should look at ALL training.
In my defensive tactics curriculum I have a saying that I usually use to describe the difference between traditional martial arts and practical fighting skills: "You don't have to fight like me; you just have to fight well." The same concept applies to what we show on TBD. Take what we present as a starting point and adapt it to your skills, your physical attributes, and your situation. As long as you have a proper, effective, and consistent solution for the problem that you can apply under stress, you're good. That's the best way to maximize the odds of saving your butt.
Stay safe,
Mike