It would be incredibly complex to build your own Dropbox. Maybe it wouldn't be "complex" to use rsync to automatically copy files over to some other drive if that's all you wanted, but Dropbox does way more than that and I don't plan on dropping Dropbox for some half baked solution that requires more effort to set up, maintenance and ends up in lost data because on the one in a million chance the FBI might want to look at pictures of my pets.
I don't know how I feel about government surveillance, but I sure as hell don't see it worth to trade some supposed imperceptible theoretical harm with tons of actual effort and inconvenience.