Having my DL info printed on my checks is a far cry from your idea. I'm paranoid, too, but I try not to get carried away with it.
If I read this right, the pizza guy asked for the DL #. I always make one up on the spot. And when ever someons asks for my birth date it is always today.
I used to make up phony SSNs too, but Big Brother has tied too much stuff together and you have to be careful or you'll get caught. My Favorite SSN was 123-45-6789. Never had anyone qusetion it.