Ace Elevator was awarded the contract to modernize the elevators, changing from the original pulley system, to a computerized system. This work was completed in March, 2001 I believe. If the power went out in the towers, when the power was restored, the elevators were to be brought back online sequentially (I'm not claiming Ace Elevator had anything to do with 9/11).
I am in full agreement with the electrical engineer interviewed about an hour into the film. He was there when the buildings were built, and his assessment of the elevator shafts, and who might have had access to them is very interesting.