Your QF friend really shouldn't be discussing the details of staff travel with non-staff members... but that aside, they're incorrect.
Qantas now start processing upgrades up to 7 days prior to departure with most (if not all) finalised by the night before departure. Staff do not BOOK tickets, they LIST on flights as a standby and only get on-loaded if there are spare seats.
I'll give an example. Say a SYD-LAX has 8 seats in Y and 2 in J available at the start of check-in. This flight is considered to be heavily booked and staff will not be accepted for travel until the flight has closed. So while you're sitting onboard already (sparking wine in hand!), the staff are standing outside at the check-in counters waiting for the final load to be completed (this includes the loading of commercial cargo, as it is a higher priority than staff). Then, and only then, will the staff be on-loaded (and will rush through security to be the last onboard the aircraft).
In another case, a BNE-SYD has 100 seats in Y and 8 in J available. The staff member will check-in and be issued with an Economy boarding pass. Once all passengers are onboard, they may be upgraded to business if there are any empty seats left in business. Again, everyone else is already onboard and there is no chance of a passenger buying a seat or upgrading to J.
Business is not free to staff members. They pay extra for the privilege of possibly sitting in business and this can be a big expense. For domestic flights, if a staff member books and pays for a business upgrade, they do not receive a refund if business goes out full and the forfeit the money (which can be over $100).
Duty travel is different as the crews are entitled to travel in business while they are travelling for work purposes only. That said, only a limited number of seats in the cabin are available for duty travel (generally).
So no, staff are not given any priority at all over passengers (I'm not going to say paying passengers, as the staff are paying as well - often just as much as some passengers are). Staff are the lowest of lows when it comes to on loading.