It used to be much easier for illegal immigrants to get drivers licenses. But really it depends on what state you live in. You don't have to prove you're a legal resident to get one in some states, or didn't before 9/11. In NY State you need a legal mailing address and a social security card, but those can be faked and indeed there is a whole faking credentials for illegal immigrants industry.

The accent is really a much better argument ;-)