I think that the difference is that the RIAA can't look at your GMail account, so they can't know that you have that MP3. Therefore, they will not file a takedown notice.
BUT... (there's always a but =P ), what happens if you upload a video to YouTube, and you save it also in your gmail.
If someone files a takedown notice on that video, should google also delete from your email ? should they also delete it from every other gmail account that holds a copy of that video? Oh man, this is getting complicated...
Files in your gmail are not public. Likewise, files in your Dropbox are not necessarily public. I don't see the problem with removing public links in response to a DMCA takedown, while still allowing private access for those people who uploaded it.
The difference is Goole's relationship with the music industry - this has nothing to do with laws and everything to do with Google's ability to set the agenda.