The narrative he was trying to create was that the military literally considers our presence in the Middle East as a crusade, in the historical sense. And frankly, I don't think this is too far off.
George Bush used "crusade/holy war" rhetoric both publicly and (reportedly) in private. Religious indoctrination in the army is rampant. Eric Prince of Blackwater has been accused by former employees of trying to start a Crusade.
So what's your counter narrative? The higher-ups in JSOC and the military are all reasonable secular humanists?
The Pope is a member of the Jesuit order. This doesn't mean that the Jesuits have "infiltrated Catholicism", it just means the Pope is a Jesuit. If you think that Opus Dei and the Knights of Malta are "shadowy conspiracy groups", you need to stop reading Dan Brown books, and start embracing the fact that other people have different ideologies.
As far as your "appeal to authority" is concerned, yes, that's exactly what it is. That's how journalism works. Anonymous sources get quoted all the time for pro-military stories. Deal with it. Would you have criticized Bob Woodward and Carl Bernstein for using "anonymous sources"? Part of good investigative journalism is relying on the reputation of established journalists. And while you're right that this is an appeal to authority, your argument is nothing more than an ad hominem designed to discredit the narrative Hersh has created.