It turns out that the only argument William Witt has for defending a distinction between the AC and the PAC (for definitions, see this post) is his belief that there is a legitimate epistemological distinction to be drawn between the mental state of an eyewitness to an event and the mental state of someone who was not an eyewitness to an event but who believes the same thing as the eyewitness.
There is a rather famous passage in Plato's dialog Theaetetus that explores this very issue while considering whether or not "knowledge" ought to be defined as "true belief". At 201a-d Plato has Socrates present an argument along the following lines. Imagine an eyewitness who testifies truthfully before a jury, and the lawyers, whom we all assume to be decent, honest folk (just use your imagination a little here folks), do a good job of eliciting the testimony, and the jurors all come to believe the testimony of the witness. So now both the eyewitness and the jurors have mental states that could fairly be described as "true belief", but we are asked whether or not the mental states are the same. It is tempting to say that the eyewitness actually has a different mental state than the jurors, because if either side has "knowledge" of what happened, surely it is the eyewitness, and not the jurors, because the eyewitness actually saw what happened (and therefore "knows" it to be true?) while the jurors have merely been persuaded, by the eyewitness's testimony, to believe that it happened. So, the argument claims, knowledge cannot be the same thing as true belief.
This would be a neat little argument were it not for the fact that Plato has just spend literally half of the dialog proving that knowledge cannot consist in sense perception, and yet the only difference between the mental state of the eyewitness and that of the jurors is that the eyewitness's mental state is "corroborated", in a certain sense, by sense perception. At least in terms of the semantic content. It turns out that Plato's principle objection to defining knowledge as "warranted true belief" is not that "warrant" is ambiguous but that knowledge cannot be a kind of belief, at least not on his accounts of knowledge and belief. Knowledge is something that is already present in the soul, according to Plato, and experience does not constitute it at all, it just brings it to the surface.
So what, then, is supposed to be the difference between the AC and the PAC, according to Witt? The difference is that the AC has a leadership that actually witnessed such events as the Resurrection. This is supposed to give the Apostles greater "authority" to teach what they teach. Witt never considers the rather paradoxical problem of the Canon of Scripture from the point of view of his own claim, since he appears to take the Scriptures rather seriously even though none of the texts contained in the New Testament was actually produced by one of these alleged eyewitnesses. Be that as it may, we may still wonder what, exactly, the Apostles had that they were not capable of "handing on" to their successors.
This is an interesting problem for Witt, who is an Episcopalian and, hence, ought, if he is being a good boy today, to believe in the Apostolic Succession. Perhaps Apostolicae curae makes him nervous, but I doubt it. If the Apostles possess anything that they were not able to pass on to their successors, it seems that the only candidate would be something like the experience itself, since clearly they were capable of, and one hopes successful at, passing on the semantic content of their beliefs about what they had experienced. And yet, anyone who has watched, with even a moderate amount of skepticism, anything like an evangelical revival meeting--you know the kind, the sort where folks are literally "revived" from all sorts of maladies--anyone who has witnessed (if you will pardon my use of the word) such things will know that even large groups of people can be rather grossly deceived about the nature of what they are witnessing. So if the Apostles had any kind of authority deriving from their status as eyewitnesses, it cannot be due to the simple fact of their having experienced certain things, but was due rather to the fact that they were granted a special charism with regard to interpreting their experiences, for example, in determining whether they were real and what they might mean. This task of interpretation, however, is clearly a propositional one, and as such can indeed be handed on to one's successors and, if there is such a thing as a charism at all, it is quite possible for one's Successors to have the same charism of interpretation even independently of whether one's Successor is or is not himself any kind of "eyewitness".
In short, Witt's ecclesiology is grounded in a very naive and, indeed, hopeless, epistemology. He has yet to meet the argument against the distinction he draws, though to judge from appearances he neither cares nor intends to try. That is a pity, even if it is unsurprising.