The Upset That Led To The Murder of U.S. Diplomats

It appears to be primarily because something that has long been acknowledged by Muslims (until it became Politically Incorrect) was mentioned in the video: that Mohammed married a girl of nine.  And I don't mean betrothed; that happened at age six. From Muhammad Abdul-Rauf's The Islamic View of Women and the Family (1993):

But he was also kind and tender with Aisha, who lived with him nine years before she was widowed at the age of eighteen.

Fawzy Al Ghoudairy's Why Did Prophet Muhammed Marry Aisha, the Young Girl  is entirely devoted to establishing

that such marriage in such age in such era was a natural matter, therefore it is clear that they not criticizing the early marriage of a nine-year-old girl to a fifty-year-old man as much as they are keen to criticize and distort the picture of the Prophet of Islam.

The older a book is, the more likely it is to point out this inconvenient truth, such as J.D. Bate, "The Wives of Muhammad," Indian Antiquary 7:93-94 (April, 1878):

Muhammad's third wife was 'Aisha, usually written A y e s h a, and less frequently A s h a. 'Aisha was the daughter of 'Abdu-1-lah binUthmiin Abu Qahafa, better known in Moslim history under the name Abu Bakr (lit. ' the spinster's father'),—a title which was bestowed upon him in allusion, apparently, to the fact that he was the father of the only spinster whom ' the prophet of God' had taken into his haram. It is not ascertainable at what period this name was given to the father of 'Aisha; most probably it was not given till after the Hajira, when the marriage toMuhammad of such a large number of widows would give distinction to the circumstance of 'Aisha being the only one among all his wives who had been married to him in her virginity,—a circumstance of which 'Aisha never failed to boast. She was the most youthful of his wives, having been married to him at the age of six years, and Muhammadan historians relate that 'the prophet of God' consummated his marriage with the child when she reached her ninth year (Arab, sulibut, ijtima',)

Recently published books also treat this rather matter-of-factly, such Kecia Ali's Marriage and Slavery in Early Islam (2010), 76:

Rather than having a strict age-based limit, or one dependent on menarche, the determination of female readiness for sex (and thus cohabitation and support) hinged on physical sturdiness and appeal to men.  Appeal is occasionally mentioned, however.  The age of nine appears sporadically as a minimum for consummation, majority, or both.  This is presumably tied to the hadith, quoted by Shafi'i, that Aisha's age at nine when Muhammad consummated their marriage.  It is possible, though I think highly unlikely, that the causal link goes the other way--that is, that the hadith are an attempt to justify consummation from the age of nine.