I have to agree on the no fine-grained control. My point was that it is easy to opt out of the notifications by email in general. I'm positive that there is an option where you receive a notification when someone send you a message, but I don't think it is possible to get event invitation notifications only.
For instance, how do you easily configure Facebook to ONLY send you emails when you're invited to an event or someone sends you a Facebook message, but NOT when your friends post random stuff?