I think Mitt Romney (at least 2010 Mitt Romney) and I can agree on a few things vis-a-vis the whole Terry Jones movie/riot/assassination/political-fallout situation:
1. Terry Jones has an absolute right to release any video or other form of speech he wants without interference from the United States government.
2. Doing so in the current environment puts Americans' lives at risk, most of whom are not Terry Jones.
3. It is a fundamental agreement we make with each other as Americans, in the form of the 1st Amendment, that #2 does not invalidate #1
However, there is not, so far as I'm aware, a constitutional protection from the government refuting or opposing your freely-spoken expression. If I say that Queen Elizabeth is actually a dude, and London asks the American Embassy if that is the official position of the American government, of course our ambassador should be allowed to answer the question. Similarly, if the Egyptian people are angry at the US government and its Embassy over Jones' film, the Embassy is fulfilling its duty under Article 3 of the Vienna Convention on Diplomatic Relations (.pdf) of "representing the sending state in the receiving state" and "promoting friendly relations between the sending state and the receiving state" by making clear that the content of the film does not represent American values, even if allowing its existence/distribution is a founding principle.
The statement from the Embassy clumsily tried to make that distinction, condemning the film while also reinforcing Jones' "universal right of free speech". The statement took an unnecessary shot at Jones and his partners, calling them "misguided", and mentioning the 9/11/01 attacks didn't really contribute anything. It would have been much better if the author, who was explicitly told by the State Department to not release the statement but did anyway, would have deleted those parts and included a little more about why we weren't presenting the mob with Jones' head on a platter. But of course it's proper to condemn the attacks on the host country's religion.