Dropbox and privacy are core to its mission
Wrong.
If anyone thinks Dropbox, or any other hosted storage system has privacy as a core function is major league delusional. I use Dropbox all of the time. For stuff that isn't intensely private - including encrypted sparse images. I think Dropbox or it's ilk is OK for everyday use, but if you want something private, keep it under your control.
Not that I think having Ms. Rice on the board makes any kind of sense unless you are trying to suck up to the Powers that Be and get in bed with everyone else (for the dollars, of course).
But look at the bright side of things - they could have asked Larry Ellison.