I seem to recall that a guy posted footage he'd taken with his cell phone while visiting the foyer set for the Depp/DS film - and he did so on a private Web site where only people who'd been allowed onto the site by him were allowed to see it - yet he was forced to take it down. So apparently Lynch and Burton are cut from the same cloth when it comes to even seeing sets.
But so far as supposed spoilers go, the article shows that even the Twitter account holder where the TP info was being tweeted used the word "spoilers" when he tweeted: "Word has just reached me that David Lynch is not pleased with spoilers coming from the set. To respect David and Mark, we will stop at once." So I suppose that and the article's use of "full-on spoilers" would seem to indicate that more than just a few photos of the sets and what have you was being tweeted.