This may be a dumb question, but if someone took a piece of copyrighted data which is illegal to own without paying for it (let's say a ROM of Super Mario Bros.) and inserted it into a transaction with a high enough fee for miners to bother, what would happen? Would having a copy of the whole blockchain on your hard drive become illegal?
The claim of injury from a copyright violation must be directed at a specific party. They might be able to sue the person that put it there, but no one else would really profit from the existence of this, and they would be hard pressed to show how this was damaging. Also, I think the court would appreciate the amount of technical expertise it would take to store/remove any meaningful amount if data from the chain (that is, you must be adept to convert block chain data into other media formats). That is, if the data were posted, most users would be unable to actually access it.