with short-links redirecting to the file, it could be done with url shortener with stats, it's just more convenient generating them with this service I guess
correct. it was very inconvenient every time you need download stats to open bit.ly for that.
The Dropbox auth. page states: "This app will have access to your entire Dropbox.
Please make sure you trust this app before proceeding."
Does this really need access to the entire Dropbox? Why should I trust the person who wrote this?
To get stats for bit.ly you can just add a '+' symbol on the end of the short link: http://bit.ly/owigAj+