Why does it need access to all websites in addition to dropbox? Seems odd.
1) Your data on dropbox.com and www.dropbox.com
2) All data on your computer and the websites you visit
#1 is obvious. I think it needs #2 so it can save a copy of the older version to disk and then launch the diff tool. If you want to check out the extension before installing it, see http://superuser.com/questions/337172/how-do-you-do-examine-...