I'd be seriously questioning their competence if they'd only looked at direct flights!
In many cases, that's what ground crew do. More so when they have a large amount of people to get through.
I've had 2 flights which have had to be rerouted. First was QF CBR-SYD-NRT. SYD had weather issues for most of the day and all the CBR-SYD flights were delayed. It was getting to the point where I'd miss the connection to Tokyo and approached ground staff about it. They were "oh, we'll just put you on what ever flight is ready first" until I pointed out the connection, at which point, their plan was to get me to SYD, put me in a hotel overnight and transfer me to the morning JAL flight. It wasn't until they saw that the JL flight was full that they started looking at other options. I ended up with CBR-MEL-HKG-NRT (after their first option of JQ MEL-DRW-MNL-NRT).
Second time was US CAE-PHL-LGA. Weather and ATC delays were impacting almost every flight out of CAE. I noticed the issue before the ground staff did and had looked up other options and was heading to talk to someone when they asked for anyone with connections to come talk to them. Ground staff were blind to anything other then CAE-PHL-LGA, even if that meant putting me in a hotel in CAE or PHL. They did not even think about options into JFK until I pointed out the CAE-CLT-JFK flight.
They would likely have pulled up the booking of the pax they were dealing with at that time, seen where they were going to, and simply looked for flights to that place. If the pax were going to somewhere other then SYD, it seems more likely that the staff would think about other options then a non stop to SYD.
I find it hard to imagine that across QF10, all the EK flights to AU, and the possible EK-QF connections at SIN, BKK, HKG and TYO, that they couldn't find enough seats even with the high volume at this time of year.