Trusting facebook to prevent Eve from accessing to your data is not the same thing as controlling Eve's access to your data.
The usual counter-argument to this is that it isn't worth it to care about such relationships anyway, and that you should only be concerned about close friends. It is true that close friends are important, but it might not be true that the optimal strategy is to care only about them. It may be useful to keeping distant connections with old friends in case you ever run into them again, or to have a large distant social circle with diverse backgrounds and physical locations to get more diverse recommendations, opinions, help, etc. More dramatically, say you arrive in a new city where you don't know anyone and no one knows you, but most people use Facebook: if you insist that people that don't initially know you should use your favorite communication medium rather than Facebook to interact with you online, it might be harder to get things started.
This isn't to say that you should use Facebook: I never used it and discourage people from using it. This is to argue that you should be conscious that not using Facebook may come at a personal disadvantage. I personally still think that it is more important to stick to my principles and make an insignificant effort to improve things by not being on Facebook, but I can understand that other people might think differently (though I disapprove their choice).
I have deleted by FB account twice and then I was spending lots of time explaining why, getting weird looks from people and being left out of comments (e.g. people would post something to FB and be laughing about it later but never explain about what.. really impolite of them but what can I do? engage in more arguments).
So yeah, be honest to your beliefs, just don't expect that will translate to happiness (unless you really work on telling yourself none of that unpleasant situations are really bad). We are human beings, how we interact with others matter (even if I didn't want any of that).
No matter how strange your beliefs are, you will always find people that think similar. The world is very diverse.
It seems that FB even changes the fundamental meaning of a friend. Which is a shame and a lack of social culture.