I'm guessing here (I didn't read TFA), but people are probably more likely to keep their addresses updated with the DMV than they are with anything that could potentially lead to them being called up for service in the military. As such, to make sure that the database is as accurate as possible, it would make sense to periodically merge data from the DMV.
As for the records still being in the database, despite the demise of those to whom they refer, I'm one of those people who believes that once a record is in a database, unless it should never have been there in the first place, it should NOT be deleted. If no longer relevant, then set a status flag of some kind, but don't delete it. I'm not an American, and, more to the point, am not familiar with how data exchange occurs between state and federal government departments, but if it's anything like it is over here in the UK, when someone dies the death is registered with the local register office. That information is not automatically shared with the DVLA (our equivalent of your DMV, but just one at a national level) or any other organisation. If the US system is anything like ours (and with the added complications inherent with some government bodies being federal, some state and possibly some at even more localised levels, it would surprise me a HUGE amount if such automatic data exchange was commonplace), it's understandable that those records were not only still in the database, but were still marked as active. Would we rather they simply assumed that once a person reaches a given age that they are obviously dead and can hence have their record updated accordingly?
Obviously none of this excuses how that data merge was handled. If my assumption above is correct about the data from the DMV being imported purely to ensure that addresses and contact numbers are up to date, the obvious question that follows is why these older records led to letters being sent out. The date of birth field should only have been used for identifying records to receive address updates and, as such, if anyone born in the 1800s received such letters it would be due either to a poorly written query, or to the date of birth field already being wrong prior to the merge (or, of course both).