The term I learned for the odd, overly friendly thing you did there is "thought pattern interrupt". It's a lot like the feeling you get when you start a conversation with someone, and they respond to an entirely different statement than you made, either mis-hearing you or just ignoring what you said. You stumble a bit. There's a guy in Britain, IIRC, who did a series of shows on hypnosis and manipulation (also did some pickpocketing, I thiink). He tells the story of someone accosting him to rob him, and he replied something like, "The wall outside my house is three and a half feet high." It confused the guy, and he restated his demand. Another non sequitur reply, and the guy left, confused about what had gone wrong. That wouldn't work with a determined, seasoned criminal, I think. But it's probably workable on someone who's nervous or scared.Interesting conversation and all important things to consider based on what we do. I would not want my students blindly following my drills and assuming that they were somehow super-heros and I'm pretty certain that they do not. But, it's something for me to keep an eye on.
I think that the other side of this is worth consideration from a self-defense standpoint as well. Implied authority, at the right time, delivered the right way, could buy you time and space in a dangerous situation. The studies sited (which I read, thanks for posting) could equally inhibit the other party in a conflict as well. I used to test my ability to change the dynamics of situations with my voice, when approached by street people who were probably just begging, not dangerous, but you never know.
What happens if I say really friendly crazy things like:
Street person: Hey man, have you got a light?
Me: Have you seen the light too? Isn't it beautiful? Where are you going tonight? Have you talked to Phil?
Or
"I need for you to take two steps back! Show me your hands, please. Thank you. Now what is it that you wanted to discuss with me?"
Either could work or backfire, but I found that when someone approaches you, regardless of their intent, they expect and want it to go a certain way. By asserting authority or doing something else to take control of the engagement and redirect it, they usually start working on their exit, which is, I must say, extraordinary self defense. Must be practiced, because it could also make things worse. Fortunately, I teach in a neighborhood that makes this very easy for me and my students to practice, now and again.
Everyone trains for a reason. Most of the people who train with me are interested in personal safety as it pertains to the world they live in, things they experience or fear experiencing on a daily basis. The other actors in these scenarios are also human beings, subject to the same bias, errors in judgement, and traps that the rest of us are. I find that knowing that and contemplating how to use that knowledge is very useful.