I don't have a dog (but if I did I'd want one that refused to give the nail clippers back to the vet) although we have four cats. All our cats are chipped but they don't go far from home.
However, locally there has been a huge story about a cat that fell asleep on top of the owners husbands van. He didn't notice and drove to work, not noticing people frantically trying to flag him down. Someone notified the wife and she called him but by this time he was at work (several miles away) and there was no sign of the cat.
A huge search was started, leaflets put out. We have a great Lost and found pets group on FB in this area and a few of the admins have scanners so loads of people out looking and 10 weeks on still no sign.
Then a lady a few miles away noticed a rather thin cat with a broken tail in her garden and took it to the vets. He was scanned and found to be 'Van Cat'. He's now home, half his body weight but otherwise ok although his tail is a bit wonky! He made the local paper and is a bit of a legend round here now.
If he hadn't been chipped I doubt he'd have ever been returned home. The woman who found him had no idea of his story.