i have integrated Facebook sdk in Xcode 6 (with swift). During the login i request the public_profile permission:
FBSession.openActiveSessionWithReadPermissions(
The profile picture is in fact public and you can simply by adding the user id to Facebook's designated profile picture url address, ex:
var userID = user["id"] as NSString
var facebookProfileUrl = "http://graph.facebook.com/\(userID)/picture?type=large"
This particular url address should return the "large" version of the user's profile picture, but several more photo options are available in the docs.