After spending several posts setting the table, I never got around to serving the meal on my response to the conflict between Ross Douthat and the Catholic academics. (If you want timely commentary, read a less busy blogger).
On a gut level, I agree with Bishop Barron's take. The way to respond to arguments that you don't like it to offer a persuasive counter-argument, not to complain to the writer's bosses. I would also agree with Damon Linker's note that Douthat's commentary on the synod is a curious point at which to commence concern with the New York Times publishing incorrect or misleading information about Catholicism. (ahem).
Nevertheless, one needn't look around too long to note that public debates aren't always won by those who have the truth on their side, at least in the short run. There are any number of issues where public opinion and policy runs directly against the facts.
In many of these cases, the argument that people cling to is something akin to, "Bad people are conspiring behind closed doors against you and lying to you about their true intentions." This is an argument which, to Bishop Barron's point, is impossible to disprove. It is an argument people will cling to in the face of evidence against their position. It is an argument that drives people apart and leads them to distrust each other.
Given this, I think it is irresponsible to advance such an argument absent some solid information that this is the case.
I hasten to add that Douthat's commentary is irresponsible in the same way that much of, for example, Father James Martin's commentary about the doings of more conservative members of the hierarchy is; for example, his suggestion that the investigation of the LCWR was really just a politcially-motivated hit job. Or the notion that Pope Francis only met with Kim Davis because some conservative bishop pulled a fast one on him.
From the beginning, it appeared that Douthat's coverage of the synod was akin to how he would cover a political convention - different factions jockeying for influence to push their agendas. I understand that often when politicians say they want a "conversation," what they really want is a particular out come of that conversation, and they will use whatever means at their disposal to drive the conversation to that outcome.
Perhaps it is naivete on my part (as Douthat's mocking summary of the synod would suggest), but that is not what I saw Pope Francis doing. I saw him recognizing a pastoral problem, and getting people together to try to figure out how to address it. Perhaps he was hoping for a particular outcome, but was open to where the spirit would lead them.
Now, this is not the argument the theologians made. They argued that Douthat did not have sufficient credentials to publicly comment theologically.
So I understand why the academics responded in a way other than a robust exchange of ideas. Columnists like Ross Douthat and his editors at the New York Times do bear a responsibility regarding the arguments they advance, give prominence to, or support.
Thus, my conclusion is that there's no real winners here.