I have a funny story about strays:
I had some guests over for a cookout from my local church years ago. A lady came in and saw my big fat yellow tabby cat..she said "That cat! Where did you get it?"..I told her I brought it with me when I moved from the city ..I had it as a kitten and he was 12 years old.
She said she thought he was a stray and had been feeding him for the last month.
Another guest arrived..."That cat! Where did you get it?"
LOL...5 people told me they had been feeding him anywhere from a month to a few weeks and considered him theirs. They were shocked he belonged to me...Hence why he was so fat. Busted..he got skinny in one month after that cookout..
Your cool dog isn't a stray, he is a mooch. Some critters mooch food, some mooch affection...I think he is just making his rounds.