Your machine -> TOR -> hacked home user or server -> your target.
This way you only transfer the files between the target and the hacked server, and from there on to a torrent, and heck, why not let that machine seed it too.
Chances are that they even used a chain of hacked machines to get to their target. It gets pretty complicated pretty quickly if you (as in FBI et al) have to raid several companies to get your hands on machines to do forensics on.
I doubt these files (or much of anything else) ever touched the criminal's physical machine. Unless, of course, they fucked up by, say, posting to pastebin or a tweet or something else that is seemingly insignificant (at the time) using their own IP.
Most tend to.