"Tell you what, we both go to the same summer camp, so we can be camp friends. But if I see you at school, I won't admit that we are friends. If you try to bring it up, I'll deny it."

Facebook is always biased towards sharing information, instead of respecting privacy. They also apparently don't have the technical ability to keep private things private, as shown by the multiple leaks of Zuckerberg's information. When was the last time that Larry Page's gmail was hacked?

In any case, I disagree with your point. I think if either party makes the friendship private, it should be private.