You still have to trust them that they do not transmit your keys elsewhere and that they really do use the same crypto code thy open-sourced.

I am not saying that you can't trust Dropbox. Quite on the contrary. But if you give your key to some unknown entity, you have to trust them. You can choose to trust their claims about what they do with it, but there is ultimately no guarantee.

Beauty of asymmetric crypto, you don't have to trust them as soon as you can trust the client software (that it doesn't do something nasty with your private key/pass). And having an open source client can actually provide that trust.