WOW! I have traveled all over the United States and Canada and authorities have ever asked for anything about the dog. A few campgrounds have asked for the rabies certificate. There are no entry points within the United States or Canada- just the expected border crossings.
I always travel with my dog's complete medical records. They came in handy one terrible day when my 8 year old Golden became suddenly and seriously ill. Even though she did not survive, those records were invaluable in treating her and preventing repetitive tests.