I don't store any files on my Dropbox account that even remotely resemble anything owned by media companies, so I suppose the risks are negligible for myself. Using something like EncFS on top of Dropbox wouldn't hurt, either.
Other people might not be as lucky. People in some countries could store and share files that are completely legal to distribute where they live, but still protected in the U.S. For example, copyright expires 50 years after death in Canada, compared to 70 years in the U.S. If an American company issues a blanket takedown notice and Dropbox obliges, Canucks may be adversely affected. Besides, humans make mistakes. What if somebody pastes the wrong hash into their takedown notice and Dropbox staff forgets to check it?
So even people who never violate any copyright might have philosophical objections to unilateral takedowns like this. It is important to avoid alarmism and hyperbole, but that doesn't mean that there's nothing to worry about.