Although calendars are printed for planning purposes, they are based on estimates of the visibility of the lunar crescent, and the Islamic month may actually start 1-2 days earlier or later than predicted. source
Here is another site
Eid-al-Adha: The moon's conjunction is on Wednesday, January 21, 2004, at 21:05 Universal Time, i.e. 4:05 pm Eastern Standard Time - 1:05 pm Pacific Standard Time. On January 21, the moon is going to be 4 hours old and cannot be seen anywhere in the world. On January 22, it will be seen in most of the world excluding Asia and Europe, as shown by the visibility curves. Therefore, first day of Zul-Hijja is going to be on January 23 in most of the world, and accordingly, 10th Zul-Hijja is going to be on Sunday, Februay 1, 2004, insha'Allah, while 10th of Zul-Hijja in most of Asia and Europe is going to be on February 2, 2004.
If having the moon be in a certain configuration is a prerequisite before taking action, then it would make sense for them to launch the attack a day or two after the estimated date just to be sure.