I agree that the guy might have good intentions, but I can guess at the reason for the rule. With so many people crammed into a car, and all the noise and jostling around, it’s safer to have a dog in a carrier to avoid any incidents that might happen.
(Not to mention the person who insists that they just have to pet the puppy, with or without the owner’s permission… I had that happen once when I was walking my Danny on a leash. He was generally very well-behaved, but some idiot tried to dart forward and pet him, even as I was telling him no. With some stranger making a fast move at him, Danny growled and snapped. Nothing more happened, because I was quicker… yet if the guy had gotten bit, Danny would have been blamed, or worse. So the rule protects the animals as well as the humans.)