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This type of behaviour shouldn't be allowed by apple, they just don't care.
I am really more and more convinced that big companies don't really care about our privacy and security.
This is a serious issue, that has been documented for a while.
http://applehelpwriter.com/2016/07/28/revealing-dropboxs-dirty-little-security-hack
Can someone test this in Sierra?
Why this is not news?

You're misinterpreting what 'Allow the apps below to control your computer' means. Granted, the wording in System Preferences is a little ambiguous. But it doesn't literally mean it can take mouse/keyboard control at a whim.

Because OS X is so locked down in the newer iterations with features such as System Integrity Protection, applications will need this sort of thing enabled to access/edit system permissions. Basically to do anything. This is not unusual.

You can see a detailed explanation here of why it's necessary and how this being enabled actually ensures data security, rather than the other way around: https://www.dropboxforum.com/hc/en-us/community/posts/204505875
 
I just did the trick to not allow this behaviour and dropbox works normally, it seems weird to me to request this kind of shady authority.
The response in Dropbox website is very light. I also don't like that dropbox never asks for this explicitly.
 
Dropbox has always been using unconventional workarounds to integrate into the system. As far as I know, the Finder extension point in Yosemite/El Capitan was created largely because of what Dropbox did in the past. Rather than going through the trouble to actually use the system panels for this, they rather install a privileged helper to add themselves to accessibility settings whenever they want, presumably to avoid that some users may not allow this.
 
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