Even more crucially, this is actually *confirmed* on screen when, in the climactic battle, the Capaldi incarnation is explicitly refered to as the thirteenth one. No ifs, no buts. Go back and watch it again.
No he's not. Go back and watch it again. The Time Lord says that there are 13 of them, he doesn't say anything about numeration or about the 12th Doctor.
But anyway, the point is moot. As has been said, the showrunner decides how these Doctors are supposed to be referred to, and whatever is decided is fine with me.