A Sceptical Rule of Thumb
What is interesting about this story is how many people were responsible for destroying the library of Alexandria. The three best known candidates are Julius Caesar, the Caliph Umar, and, of course, Archbishop Theophilos.
Of the three stories the best is Umar's. After Egypt came under Muslim rule, he was supposedly asked what was to be done with the library, and replied that books which disagreed with the Koran were false, books that agreed were superfluous. So they burned it. Like the other two versions—Caesar is supposed to have destroyed it by accident in the course of military operations—there is no good reason to believe the story is true. You can find a detailed account of the different versions of the destruction of the library and the evidence for and against each at Wikipedia.
Why so many stories? The answer, I think, is clear. The destruction of the greatest collection of classical literature ever assembled—much of it now lost forever—is a dramatic event, and one that provides a useful setting for an attack on whatever person or group you regard as particularly barbarous. That is the function the story serves in both the Christian and Muslim versions. The Julius Caesar story may perhaps have survived from pure literary merit—there is something dramatic about so important an event happening by accident in the middle of a battle. Think of it as a post script to the killing of Archimedes at the end of the siege of Syracuse—by a soldier impatient at the unwillingness of the mathematician, absorbed in some theoretical problem, to come when ordered.
All of which brings me to my simple rule of thumb: Distrust any historical anecdote good enough to have survived on its literary merit. It might be true. But it might equally well be a guess or a lie or a mistake by one person, spread by many others—and getting better at each repetition. I got to observe the process at first hand in a long-ago Usenet argument when I discovered that a period reference to a woman who, in the battle of Junain, "had a dagger which she carried about" had morphed to "tied a dagger around her waist abover her pregnant belly and fought in the ranks of Mohammed and his followers" (modern Arabic speaking feminist) to "with an armory of swords and daggars strapped around her pregnant belly fought in the ranks of Mohammed and his followers" (modern English speaking feminist) to "one of the Prophet's wives was renowned for winning a cavalry charge when eight months pregnant, ..." (Usnet poster).
And, for a final example, consider the phrase "rule of thumb." According to a popular story, it originated with the rule that a husband was entitled to beat his wife so long as he used a stick no thicker than his thumb. In fact, no such legal rule ever existed. The origin of the story seems to be a comment attributed to an 18th century judge and ridiculed by his contemporaries.
P.S. A commenter points to a devastating review of the film. Not only is there no evidence that the mob that destroyed the temple of Serapis burned any manuscripts at all, there is no evidence that, by the date of the destruction, there were any manuscripts there to be burned. And the movie has altered the historical facts in a variety of other ways, all designed to serve its message, converting a rather unpleasant political squabble between two civic factions into a grand story of the suppression of knowledge by Christian fanatics.