I saw too many dog movies as a child with someone in a courtroom trying to prove the dog was theirs. For most dogs this would be pretty easy, they come running up the their true owner, but with Yorkies, they are lots more fickle, and probably think you want to brush them, so they would run to the stranger.
Joey's been chipped, millions of dogs have been returned due to this technology. It's probably more important if you travel much with the dog, or you live in certain areas that could be prone to natural disasters, but I love the peace of mind it gives me.