Just my 2 cents worth...
If, let's say, I was a bus driver, and being such, I transport hundreds or people from points to other points within my route while doing what I'm supposed to do as a bus driver. If somewhere along the way, a fugitive gets on my bus wearing a disguise. Since I don't ask for ID when someone gets on the bus, I have no idea that the person who boarded was wanted by the law, and having a disguise further reduces the chance that I recognize him. Then, I get stopped by the police who were shadowing the fugitive, who then board the bus and arrest the fugitive, which, of course, I allow. Am I or my bus company liable for allowing him passage on my bus? Absolutely NOT...
Ok, let's now transpose...
The bus driver is the owner of Hotfile and the bus company is Hotfile. The fugitive is the pirated material, and the disguise is the copyrighted material that was renamed to hide its identity. Having no file index, HF has no idea what's being stored on their site, just like the bus driver doesn't know who his passengers are. So, just like the above scenario, how could HF be liable for allowing illegal materials to be stored on their site when they have no idea what the materials stored on their site are?
They cannot just "assume" all popular material to be illegal, just like you cannot prejudge a certain color of skin to be a more superior grade of human than another color. They obey takedown notices promptly, so they can't be guilty of obstruction. So what are they (HF) guilty of?
There's a saying that ignorance of the law excuses no one from prosecution. In this case, HF isn't ignorant of the law. They know what the law provides for. They know what the materials deemed illegal by the law look like, assuming they are still in the condition that they were when they left the media companies. But having been chopped up, processed, re-processed, repacked and renamed, they couldn't have known with 100% certainty what they are by merely looking at the filenames. Even MD5 hashes wouldn't work anymore.
I'd be amazed if a farmer could still recognize his cow accurately after the animal had been turned to hamburger.
I believe that the MPAA people know that they are holding a case that barely holds water, so what they're doing is trying to bluff the opponent into folding his hand. They think they might just be able to scare the people they're accusing into settling the case out of court with their bullying tactics, since they know they have too weak a case to win legally.
This is only my opinion on the matter. I may be wrong, but this is what I believe based on what I've read, and I believe that it's not illogical, nor is it implausible.