It scared the crap out of me when Dropbox asked if it wanted to save my screenshot. Since when did it have access to things like that? I had a phone interview with Dropbox a few weeks ago and they mentioned a ton of new products that seemed vaguely offputting as well. After the screenshot prompt, I immediately uninstalled Dropbox, but after a few days I realized it had a bunch of useful backups so I ended up reinstalling it.
If the dropbox program is running under your user account, it has the same permissions you do. Unless you're on Linux and have restricted it via AppArmor.
Isn't that behavior -- asking to do something before it does it -- the behavior that you'd like? I would be upset if it went ahead and did that, and then I discovered the feature later.
Maybe if I wanted to save my screen shots. I didn't want that behavior at all and it surprised me that it had access things outside of the well-defined folder I had already known about.