Frankly, Dropbox management has no one to blame but themselves on this one. They not only had the poor judgment to release new terms of service less than 10 days after leaving their users' data accessible without password protection, but doubled down by issuing the changes on the Friday before a three-day holiday weekend. That allowed the echo chamber of the tech blogosphere to have a field day with the company's little update.
In an even bigger mistake, Dropbox execs let the lawyers write the new terms of service. So, the same people who would happily argue that loading an application from disk into memory would qualify as a possible copyright violation if the publisher didn't grant you that particular license are now in charge of protecting their client, Dropbox, from possible lawsuits from you, the actual customer and presumably copyright holder.
So, the terms of service say, "By submitting your stuff to the Services, you grant us (and those we work with to provide the Services) worldwide, non-exclusive, royalty-free sub-licenseable rights to use, copy, distribute, prepare derivative works (such as translations or format conversions) of, perform, or publicly display that stuff to the extent we think it necessary for the Service. You must ensure you have the rights you need to grant us that permission." I think we can all agree that to store, backup and let me retrieve my stuff, Dropbox would need a license to use and copy that stuff. That license should be non-exclusive--I may want to license someone else, too--and royalty-free since having Dropbox pay me for the right to store my stuff doesn't seem like a good business model.
I have a bit more of a problem with performance and public display licenses, but I'm sure some lawyer thought retrieving a file over the web at a public kiosk constituted a public performance. The key here is the phrase "to the extent we think it necessary for the Service." While I'm not an attorney, I've worked with enough of them to know that if Dropbox took the photo of your puppy and used it in an advertising campaign, as one blog comment suggested, an expensive lawsuit would ensue. Try anything a reasonable man wouldn't consider necessary to run Dropbox and lawsuits will run rampant.