To me; it would make sense if Dropbox stored everything encrypted (as in, encrypted pre-transfer), and you needed the private key to decrypt stuff, unless you specifically state that it is to be public. It just makes sense from a liability statement. That said, you can do this anyway as recomended in this article. (http://lifehacker.com/5813873/how-to-add-a-second-layer-of-e...)
You can say that google might leak your emails, but the same is true if you use your private email server.
That's still wholly untenable for the real world, but not all paranoid people live in the real world per se.
Grandalf's point is extremely well taken. It's actually true. Not only that, but regulated companies (in health care and finance) that have a reasonable belief that any of their systems might have had Dropbox on them technically need to audit now.
I point this out not to bag on Dropbox, but as an illustration of how sane some unreasonable-sounding IT policies (like, "you don't get to install random software on your desktop") turn out to be.
† (Or Tarsnap or SpiderOak, for what it's worth.)
(WebDAV isn't "support," when you look at the Dropbox/SpiderOak feature set.)
Another thing to do would be to change the design of the authentication process so that it is more inherently fail-closed. For instance, you could encrypt/decrypt the database ID of the user with a key derived securely and deterministically from the user's password, perhaps (just to keep the code simple) after verifying the password against a secure password hash.
illustrated example: billgates twitter account: " Do you want me to give you all my money or what lolz" techcrunch : "OH MY GOD, BILLGATES PLANING TO GIVE A WAY ALL OF HIS MONEY" and later : "OH MY GOD, HERE'S THE GUY BILLGATES WAS TALKING ABOUT" I mean seriously, I just hate buzz seeking journalists.
If this happens, let's look forward to a trove of blogposts about "how to make dropbox secure" from armchair CTOs, just like we saw with Twitter and the string of posts around "How I'd scale twitter" Sharding! Webscale!