This article by Dr Hawass in Al-Ahram Weekly is a couple of weeks old, but I'd missed it. I've reproduced the key paragraph below, but this link will take you to the full article.
Some people believe that Tut was the son of Amenhotep III because he is mentioned on monuments found at Thebes. Also, the hieroglyph for "king's son" can be translated as "son-in-law" or "grandfather". But it is important to understand that when Tut became king and moved to Thebes, he could not mention the name of Akhenaten. The priests of Amun hated Akhenaten for changing the religion to the worship of only one god, Aten, and for moving the capital from Thebes to Tel Al-Amarna. After the death of Akhenaten the religion returned to the old ways and the priests of Amun regained power. Therefore it is most probable that Tut, on his monuments, wanted to identify himself with his powerful grandfather Amenhotep III. Hence, the hieroglyphs on the monuments found in Thebes that read: " son of the king " can be translated as " grandson of the king ".