Excellent story. Of course, i am apologetic that you had to have the experience at all. It sounds obvious that without the presents of your sidearm the situation could have escalated to that "yucky" place. And YES - I follow your logic in thinking this man had no reasonable reason to approach you and your family in a dimly lit parking lot.
Wow-must have been VERY uncomfortable with your family there. I suppose you always picture yourself only having to ever defend yourself. That scenario, you all were in would pretty much be "Worse Case" In my mind.
I am thankful you were able to protect your family: with a show of force ONLY.