Privacy settings in social networks

I explored Facebook. There are a few settings that you can make private or public to varying degrees. The thing that intrigued me the most were the privacy settings in FB for the apps/games. The apps can get your persoanl information also and post on your behalf. You can select whether or not you want things posted about your game play to friends, to friends of friends, to all, or just to yourself. There have been a number of times that my friends play games and I get posts from them. I learned how to hide those posts. I also learned by looking at my settings that there is an anonymous log in for apps. However, this is one thing that I found that is a bit scary:

Yes, when you sign up or log into an app or game using Anonymous Login, you're preventing it from receiving any of your personal info found on Facebook. However, once you start using the app or game, we can't control what info it collects from you or your phone or computer.