You won't likely find such a party in cases like this.
What is more likely is that each side will hire a forensics firm to image the drive, and as long as both their checksums match, than there isn't much disagreement.
I remember one P2P case that was swiftly dropped because of smart lawyering by the defendant's lawyers.
To deal with the "expedited discovery" bit, the lawyer himself took custody of their hard drives. As an officer of the court, he could take responsibility for preventing evidence from being destroyed. He then offered to make it available to third-party forensics experts for imaging, and they would be able to get a ruling from a judge concerning exactly which things those experts would be ordered to search for (rather than letting the plaintiff's lawyers trawl through everything at their leisure).
I'm not quite clear on how much of that is happening here. One might hope this would be the ordinary procedure, but I have to worry about any judge who signs an order telling someone to retrieve information from the internet, period. I realize it was swiftly reconsidered and amended.
For that, I give them due credit, even though I worry about any state of affairs wherein an absurd order could be issued in the first place.
What is more likely is that each side will hire a forensics firm to image the drive, and as long as both their checksums match, than there isn't much disagreement.