Actually, the library was burned during the fighting between the Eqyptians and Romans. perhaps some remnant survived that was burned in later times. In late 48 B.C., Caesar commanded an expeditionary force to settle the civil war between Cleopatra and her brother, Ptolemy. A large fleet of war galleys was in the harbor at Alexandria, and Caesar ordered the ships burned, lest they fall into the hands of the Ptolemy's Egyptians. As the great American military biographer, Col. Theodore Ayraut Dodge noted, "It was in the conflaguration thus begun that Alexandrian library perished, togerther with many other public buildings and treasures." (Dodge, "Julius Caesar", pg. 582)
According to the link you provide, Canfora's rather lowly-rated book is merely expressing an opinion on when the library was destroyed - one that flies in the face of a mountain of evidence to the contrary. Again, perhaps some small remnant of the library survived, only to be destroyed at a later date.