Does the difference make Q?

I will take a temporary break from my Mark-Q overlap series to comment a post from James McGrath on Exploring Our Matrix headed The Difference Makes Q, which argues that "While the similarities constitute the substance of Q, the differences between Matthew and Luke provide the strongest argument for the existence of Q" (emphasis original). There are, I think, a couple of difficulties with James's interesting post. James writes:

If it were simply a question of similarities, one could account for them reasonably in any number of ways - as evidence that Matthew used Luke (or vice versa), that both knew a common written source, that both knew the same oral traditions, that both heard Jesus say the same things, and so on.

No, I don't think so. The high levels of verbatim agreement between Matthew and Luke in many double tradition passages is too great for this material to be derived from oral tradition. Indeed, I would argue that it is also too great for it to be derived from a shared written source. We have an idea of the degree of verbatim agreement that they exhibit when they share a written source, in the triple tradition material, and it is not as high as the degree of agreement we see between them in double tradition material. The link between Matthew and Luke is a direct one. I will be explaining this point in a little more detail in a forthcoming blog post related to my forthcoming paper at the SBL Annual Meeting Q Section.

James goes on:

It is the differences that make it unlikely that Matthew used Luke or vice versa. It is hard, on the supposition of such a literary link, to understand how they could end up with incompatible genealogies, incompatible infancy narratives, and incompatible accounts of the death of Judas. Differences and alterations could certainly be explained in terms of the hypothesis of direct literary dependence. But agreement on large segments, with variations that make sense in terms of the alteration of a saying for particular reasons, and yet disagreement on narrative and geneological [sic] details without any obvious reason for those differences, suggests that we are not dealing with direct literary dependence and redactional alterations.

This is a form of one of the classic arguments for Q, viz. Luke's lack of M material, on which I have commented extensively in The Case Against Q. In the form in which James states it, the notion that the disagreements between Matthew and Luke have no obvious reason simply begs the question. I would want to add, moreover, that on the assumption of Marcan Priority, both Matthew and Luke make major changes to their source which result in what one might call "incompatible accounts". Did the resurrected Jesus appear in Galilee (Mark) or Jerusalem (Luke)? Was Jesus anointed by a sinner in Simon the Pharisee's house early in his ministry (Luke) or by an anonymous woman in Simon the Leper's house just before Passover (Mark)? The differences between Matthew and Luke no more witness to their independence than the differences between Mark and Luke witness to theirs.