first off, it's a lie. Any database can be searched and backed up. And how the hell does a database cost $25 million?
Have to agree. If it's on a functioning HDD, it can be backed up. In this case, probably as simple as right click + copy. The right kind of software can even scrape together data on a disk with a corrupted filesystem. These people are lying through the teeth, or they are so incompetent they don't know the first thing about what is basically computers 101.
And speaking as someone who has created tons of databases for projects of mine, what they needed was absolutely not worth 25 million, let alone even a quarter million. That kind of waste is either corruption or incompetence of the highest level, both of which demand resignations from people handling the department's money.