This is a really common arrangement when the costs involved are non-trivial. Even in civil litigation, complex e-discovery often involves cost recovery for searching through and locating records.

I had a similar experience related to a more typical criminal investigation and an individual computer. There was a warrant signed by a federal magistrate, our counsel reviewed it, and they were professional and respectful of our operational concerns.

The problem here is the secret court, secret warrant, etc. the rest is fine with me, the police should be able to investigate crime with appropriate oversight.