What does it take to get FaceBook to stop pushing notifications to my iPhone?
If there is something FaceBook is good at, it's in bothering it's users :)
So make sure you've unchecked those items:

Make sure you've switched the Notification Center-slider to off and the Alert Style to none in such a way FaceBook is listed in the Not In Notification Center.  




And if you go to Settings &lt; FaceBook, make sure you're Push Notifications are all switched off.