I suppose it still tells that service that I have a FB account. Better than telling them everything about me, I guess?
Which barely more invasive than telling them you breathe air, no?
I'm curious what happens to functions inside the app that need identity. Do they work as normal but the app developer can't see the information? Or does everything the user does prompt for a login, so the app developer can be pretty assured that nobody will go for any length of time using the app before they give up and log in?