The other day I had Gossy at the nearby city park, which also has the ball fields. We we walking quite a distance from the ball game spectators (Gossy doesn't like crowds) when suddenly this lady (maybe in her 30s) comes running up to us. "I want to see your dog!" It took me by surprise - most people if curious walk up and ask either to pet the dog or ask about the breed. So her comment gave me pause - it made me very uncomfortable. I said "Why" and she just repeated "I want to see your dog - it's a basenji right?" I was now thinking either she thinks this is her lost dog or she wants to grab it. I said "You can see her from where you're standing". She kept persisting but not coming closer (she was at this point only a few feet away) with that same comment, "I want to see your dog." I told her "I don't think so, I don't know you and I don't know what you want with my dog". She finally said she loved dogs and then said good day and finally left. Normally I'm quite happy to let a person pet my dogs and glad to answer questions. Maybe I was too paranoid about dog snatching but no one has ever acted this way before.
How weird! For whatever reason that lady approached you and Gossy as she did, you just never know what would happen so I think being cautious and following your instinct was a good move. I also tell people that my dog doesn't like strangers and that usually keeps them at bay.