I am leery about doing physical copies for the same reason, but if someone steals you car, they are already going to have your full name, home address and other info off of your vehicle registration and insurance cards.

If you do decide to carry it in your BOB, it might be worthwhile to have a small, unobtrusive pocket sewn to the inside to hold stuff like that. A thorough search of your pack would find it, but there is a reasonable chance that a casual thief would just dump the contents on the floor and grab what he wants.