I have never been asked to see my documents other than when I applied in person for a FAA PPL based on my UK one. Even post 9/11 no one seemed interested when flying with an Instructor.
I even managed to hire a PA28 without a checkride, just took one of the guys who worked in the hangar with me, again no one asked to see documents. I must have an honest face, or he was looking for the insurance money, that was post 9/11 too. It is a treat to be able to touch and go at International airports without having to stop to pay huge sums of money. Wish we could fly like that here.