I think a case could be made that knowledge that <A friend B> belongs to A and B equally and that neither has standing to preclude the other from sharing that fact. Of course they could both mutually agree to such an arrangement ahead of time, but outside of such an agreement, I have a hard time seeing the case for "B prevents A from telling C that A and B are friends".

Another aspect of this though, is "how much can A tell C about B without permission from B?" We know that IRL, people do get angry when friends reveal overly personal details about their lives to others, so this is definitely something to consider.

Agreed. And I am not arguing that it is, or should be. But the mere fact that two people are friends seems to me, at first blush, to be something that normally either person would be free to share.

I'm not sure how you got that from what I said above. Obviously there are such things. But I do think it's an open question to what extent we can compel our friends to keep things private. Of course if someone is really a "friend" you would expect them to keep confidences if requested... that's part of the definition of "friend" in my mind.