Can anyone else confirm that they do this? It's surprising to hear that--I would have expected that if something's in your private Dropbox, there couldn't be any copyright infringement at all. Aren't backups generally considered fair use?
http://www.dropbox.com/terms#dmca
As they will probably never receive a DMCA notice for your private folders they won't delete anything. (My opinion, I'm not associated with Dropbox)
edit: replaced provide with private
That said, yes, I'd expect them to stay out of my data unless I do something silly like using them as a distribution mechanism.
Obviously, but how can Dropbox tell if the files are torrented or were purchased legally without DRM? Or legally ripped from a CD for a backup?
That said, I don't think Dropbox should care.