That's not a fair analogy, because the bottle cap game does not need that information. It's more close to a doctor asking you about your and your family's medical past. If you trust the doctor its fine, if you don't it's a hard situation to figure out.
Edit: this is not supposed to be a direct analogy (obviously Facebook does not have your medical records yet, afaik). Games want to have the ability to find out who is your friend and to post on your behalf, it's not absolutely necessary but millions of people understand it's the price they pay for a free game.
What games are you claiming need the same level of information about me as a doctor?
Frankly, your analogy is ridiculous. Facebook apps aren't integral parts of my health and well-being. They don't need to delve into my personal life.
They want to. That's one way to exploit me to advertisers. But a Doctor absolutely needs to, for my own well being. Games and the advertisers they serve don't have that claim.
But how can advertisers target their ads to your special interests if they don't know everything about you? Advertisers are just as essential to your well being as the doctor is, if not even more. </preemptive sarcasm>
The social element is absolutely essential to such simple games. If it weren't for the constant nagging of your friends there wouldn't be much fun they would practically not work.
If you feel the games exploit you (or the doctor invades your life) , then avoid them.
Edit: this is not supposed to be a direct analogy (obviously Facebook does not have your medical records yet, afaik). Games want to have the ability to find out who is your friend and to post on your behalf, it's not absolutely necessary but millions of people understand it's the price they pay for a free game.