The document is supposedly from 1509- usually for something like this there's a provenance: a history of the various people or institutions who've owned it, and that's what a dealer/collector would be looking at before purchasing. We don't see that here, because it would be likely rather boring reading.

The picture is an illustration in a broken book that's much later- perhaps Hume's History of England , a book of Kings of England, or something similar from the 18th century. The engraving is quite fine, not at all like the heavy woodcuts you'd see in early 16th c. books. But the article does not claim it's the same age as the MS, or say anything about it at all, really, so they're not answerable to the charge of passing it off as a fake.

However, the illustration is taken from paintings of the later Henry VIII, the heavy, bearded , middle-aged one, and the Henry of 1509 looked like this so you could say that, in a way, it's of the wrong man.