Is this exploitable in some odd way?

What if I wanted to use Dropbox for piracy purposes (I don't, just using an easy to understand model). Could I upload a copy of Avatar.mp4, compute or find the checksum for it, and then distribute just that checksum to other users? Or distribute a file that wasn't Avatar.mp4, but looked like it to the Dropbox client? Would this effectively trick the Dropbox servers into distributing the file for more, so that I could legitimately claim to not be distributing copyrighted material, but just distributing a "magic" file that caused Dropbox to give me a copyrighted file that someone else had uploaded?