I see what you mean about the credit data access. My suspicion is that the permission to do that is hidden in the fine print of many agreements. They do similar stuff with credit cards where they will periodically check your card to see if it is valid, like for EZ-Pass. Car insurance does the same sort of thing. When you sign up, you give them permission to access your driving records, ownership info etc. That's how they can do that spooky stuff like list what cars you own without even needing to put in the VIN yourself (the industry also aggregates the data that any insurance provider has on a driver, but that much more detailed and personal).
The only way to truly end the privacy concerns around the DMV data would be to eliminate the need for the data to be collected and distributed. The government wont stop collection because they use that data in all sorts of systems for stuff like collecting fees/taxes and validating identities addresses. Data distribution could be partially reduced by making insurance companies ignore that type of data in their models. Many states would not go for this because they work with the companies to verify insurance information around mamdatory insurance laws. Plus, as long as cars are financed the banks and debt collectors need some way to track who is registering their asset and where.
That's a very generalized axiom that doesn't even define what would be accepted by a society as falling under the protection of privacy. so we could accept it as true and discuss it's limitations and scope, but the axiom itself does not address whether the 'selling' of data under the DPPA is wrong. For example, is everything protected under privacy? Can I claim that my salary should be private from the government so that I don't have to pay taxes?