Those kids and their mom sound like a bunch of goons.
It reminds me of the time I was walking without my dog and someone approached me with a yorkie and said "Is this yours?!" I said no and kept walking and they asked if I was sure. I told them I was and they were all don't you have a yorkie?! I replied I did but she did not look like that and was home. Then they ask if I want this too because I already one.
I just kept walking. I think when people find dogs, and don't have pets of their own, they're very willing to pass the animals off on someone else even if they know it's not that person's dog.