If I'm not mistaken it's just for proper smog information so when they hook it up to the computer they know that vehicle is on the dyno and not some other one.
Dunno how it works in your state, but here in N.H. OBD is part of the annual state safety inspection on 1996 and newer vehicles. The computer at the garage will read the VIN from the vehicle, if it doesn't match what's on the VIN plate it's an automatic fail. Inspection stations' computers are tied into the DMV so it'll go in their database that you failed and why.
Not an issue on 1995 and older vehicles since that test isn't part of the inspection here.