Sadly, fair use doesn't actually provide a defense against the DMCA. That's why they have to make individual exemptions to it.
See DeCSS.
Incidentally, hosting pirated files as a sting doesn't actually work outside of a torrent in most countries, and here's why.
The reason is intent cannot be proven purely from a download.
Sure, you probably are intending to pirate. But that can't be proven. You could be checking it out to make sure it's actually an illegal copy before reporting it to the copyright owner, and then deleting it from your computer. (and if someone does come to investigate, you can delete it before they get there and easily claim that very thing and the claim can't be disproven) You could be investigating it to see if the crack contains a virus, so you know whether to detect it. You could be building up a library without using the pirated software. (many people do this) As long as you do not distribute it, and do not install it, you have caused zero harm to the copyright holder. The copyright people know this. Any damages from your download are 100% speculation, and the courts have forbidden companies from collecting on them.
Back in the days of using public ftp sits for piracy, it was always the uploaders that got in trouble, and not the downloaders. After all, even if you are the copyright holder, you have to download the software yourself to see what it really is. Anyone who tries to persecute just downloading will have to gnash their teeth and admit they have nothing they can ding you with, unless they have spyware on your computer. Most countries take a very dim view of that. Sure you can try to make your software phone home to verify licensed use, but better not be any false positives...
The reason you get dinged while torrenting/peer to peering is because you also engage in distribution of the copyrighted media/software, and that doesn't require intent to be proven for damages. In this case ignorance doesn't protect you. They have proof that you transmitted parts of the copyrighted work. And as the copyright owner, they are allowed to join in to find this out.