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.