I am a natural born ("native") U.S. citizen. THEREFORE, I had to show my birth certificate in order to obtain these documents.
IF Obama was born a U.S. citizen, he too would have had to show his birth certificate in order to get these documents, and said certificate would be on file with, say, Illinois DMV and/or the State Department.
My only point is that, in of itself, having a passport or driver’s license doesn’t prove that Obama is a natural-born citizen.
Does the DOV keep a copy of your birth certificate when you obtain a driver’s license? I have no idea- but I doubt they could legally share a copy, even if they did.