You can already publicly share files in Dropbox, even with those who don’t have a Dropbox account. They have to be in your “Public” folder (if you don’t have one you can create one).
I have never actually seen anyone share Dropbox links to pirated content. I don’t know why that is (pirates seem to use all other services which allow you to upload files) but as far as I can see, Dropbox has no big problems with piracy.
I have had my Public Folder disabled twice after sharing few non-copyrighted music sets to reddit's underground. I don't think they really care about copyright, since I did in fact have copyrighted music in my Dropbox as well that I shared only to friends, but rather by monitoring bandwidth. Dropbox isn't saying out loud what exact number is, but I figure it could be around somewhere 10GB of traffic per month per user.
That might be what makes it unattractive for pirates. I think filehosters pirates use don’t have that kind of bandwidth limitation. (If 10GB is the cap, a 600MB movie could only be downloaded about 17 times.)
I think that hosters like Rapidshare have an upload quota but no bandwidth limit. Bandwidth is limited for downloaders, not uploaders. (It’s impossible to download much without paying but an uploaded file will not become inaccessible because too many people download it.)
Rapidshare obviously makes money with piracy so they cleverly encourage it without overstepping legal boundaries. Dropbox is a very different company, I don’t think it would be good for them to be seen as a tool used be pirates which is why the cleverly discourage it.
Here is a link to a file in my public Dropbox folder: http://dl.dropbox.com/u/4073000/Dropbox.txt
I have never actually seen anyone share Dropbox links to pirated content. I don’t know why that is (pirates seem to use all other services which allow you to upload files) but as far as I can see, Dropbox has no big problems with piracy.