yea they do. but they can't do anything about legit downloads.
like nightwish their official webpage have mp3 samples of their
songs, u download that, but it is legit, the RIAA can't come down
on you for that.
i think the same goes for anime, cause japanese products don't come
under RIAA protection 
besides it takes alot of resources to come down on everyone who
downloads.. its alot of time and effort, and 24 hours checks. and
it doesn't hold much logic to protect the rights of people who
don't pay RIAA for their effort.