Now that there are a few more facts flowing, this is from the Qantas Flight Info site:
Los Angeles to Sydney on Saturday 13 March 2010
Flight No. QF12
From To
Los Angeles Sydney
Scheduled Departure Actual Departure
22:30 (Thu) 22:35 (Thu)
Scheduled Arrival Actual Arrival Status
08:25 11:48 Landed
So 3hrs 23mins late fits in with a 19hr + tour of duty. The close to on-time departure from LAX would have been triggered with the initial release of the parking brake before the trouble with the tug began!