The author is concerned that the feds could subpoena the data from the company that it's being submitted to. Wouldn't this same concern apply to the feds serving a subpoena to the state? Once the data is out there, it's out there. If one level of government has it, all the peer/higher levels will have access of they want it.
It sounds like this database is the one that feeds license data to NCIC. The bigger question here is if we should be compiling and using data in the NCIC suchbas driver licenses and carry permits.
States can and do resist federal subpoenas and have more leeway in doing so. They also have enormous legal resources.
The author pointed out that one potential problem is feds subpoenaing data from the AAMVA and not notifying the state of California that it had done so. Given it's such a short article, I can't think of a good reason for why you would have overlooked this.