Not any statutory law, that I know of. The "full faith and credit" relating to marriage is obtained via court rulings. E.g., see difference in age requirements. But a legally married 13 or 14 year old is still married after moving to a state with a 16 or 18 year age requirement.
It is the full faith and credit clause. Otherwise you would need to obtain a driver’s license whenever you transit a state. I am sure that if California thought that they could get away with it they would require a transit permit. They already force people who drive in California a certain amount of time to obtain a California license plate. Yes, if you live in Arizona, which requires an Arizona license for vehicle owned by residents and used on it’s roads, and work and drive in California a certain amount, you must obtain a California license plate; but not a driver’s license. Even California won’t try that. So I can see this being appropriate.