Well, if you have been paying attention to the textual follies of the past several years, you already know the answer, one way or the other. They give the name "Ecclesiastical History of Zacharias Rhetor" to the text, but in fact they are only interested in one pericope within it: the Syriac version of The History of Joseph and Aseneth, which is also known in Greek. This is not by any stretch of the imagination an obscure text; on the contrary, papers on it are being discussed this year. If you want to read it yourself in translation, you can do so at Mark Goodacre's pages on the text. The point of the text is to get rid of the difficulty that Joseph's sons, Ephraim and Manasseh, were the founders of two of the tribes in spite of their non-Jewish mother. The topic was of interest to post-exilic Jews who were tempted to take gentile wives, an issue which did not go away in New Testament times. The matter is not entirely settled, indeed, as to when the story was written, with a minority seeing in it a Christian cast.
What is certainly NOT in it, however, are the names "Jesus" or "Mary"! So the startling decoding is to simply substitute those names for "Joseph" and "Aseneth", and QED! There's your proof.
Of course, anyone who stops hyperventilating long enough to consider the logic of this can see that it falls under the fallacy of "just making stuff up". Using similar methods I can prove that Liberace was actually not gay and that James the I and VI was the lovechild of a union between him and Queen Elizabeth I. But that didn't stop reporters at virtually every major media outlet from falling for the press releases of a man whose track record (the Talpiot Tomb, the James Ossuary, etc.) is one long string of sensationalist but at best doubtful claims. It's hard for me to decide between surpassing incompetence, wish-fulfillment, or outright malice as an explanation for the willingness to repeat claims that are just not true and which would be shown to be so by consultation with anyone in the field (textual scholarship, that is, not cable channel "documentaries"). But in any case I would support making them appear in public with an appropriately worded T-shirt until Epiphany.
Meanwhile everyone who actually knows something about the field is doing a facepalm at the thought of having to straighten the public out again. None of these radical claims has withstood examination, and this one is far poorer than most. Indeed, it is so preposterous in its misrepresentations that it is hard for me not to entertain the thought of fraud. Yet year in and year out the mainstream press surpasses itself in its gullibility. The prudent man, Christian or no, doubts these revelations on sight, but among the masses, a culture of invincible ignorance grows.