Passenger masks are deployed automatically by an aneroid switch in the cabin ceiling. Once the cabin altitude climbs through a preset limit (on the 767 it's 14,000 feet) the switch activates and drops the masks. Should the switch fail or the captain think it's warrented - the crew can deploy the masks by pushing a switch in the cockpit.
Now - some people didn't get oxygen probably because 1 bottle was missing and I WOULD GUESS at least some of the other bottles and parts of the system were most likely damaged.
It has been confirmed by investigators that the #4 O2 bottle was missing and that pieces of it were found in the aircraft. One piece, identified as part of the valve assy, was found in the passenger cabin after making a 20cm hole in the floor.
They still don't know if this was a cause or after effect.