I am surprised that Mr. Schneier didn't point out that several states include the SSN in the encoded information on the driving licenses that they issue, so any "swiping" of information from those licenses could also be a serious breach of personal information.
The first breach is the driver’s license bureau requesting your SSN which is NONE of their business.
There are data thieves within the DPS and DMV and there are crooks working there who knowingly sell REAL driver’s licenses (even multiples) to people with false “information”.
They get caught (and some like the lady in Tennessee get murdered) but it happens.
Don’t fear the restaurant or store peeking at your SSN when you don’t need an SSN to drive a car but the State wants to exert power over deadbeat dads (even if you are a woman and/or have never sired kids).