Well, what he says in that excerpt does not jive real well with the words of the people who were actually taught by the Apostles.
The folks who were taught by Peter (Clement, Mark) by John (Polycarp, Ignatius) etc. left us historical writings. Those writings—while they may not be infallible—are certainly crucial evidence to this question.
In your comment, when you refer to the "excerpt", what in particular are you referring to? Mohler's reponse, or the text from the Vatican?