How do you think AJ telling the EK staff to "sort it" is going to do anything?
I wouldn't be surprised if there was only 1 QF paid ground staff member, the supervisor, on duty at any given time with EK staff handling everything else. Are you suggesting that maybe they should have called in some cabin crew to assist with ground handling?
The last time I was at LHR, there were 6 QF service staff on duty when I went though. 4 customer service agents, a supervisor and the duty manager. The agents and the supervisor were working check in and once check in closed, those same agents moved to the gate to run the boarding process.
Most airlines have very few customer service staff working at out stations, with in many cases, the only person at a port actually working for the airline in question is a manager. That's the reason ground service companies are a thing.
That's fine when things work to plan. When something goes wrong, the airline doesn't have anyone else there to throw at the problem and the contracted company (either another airline or a company like SATS or Danta) can't throw many people at the problem either as the staff have either gone home or have other work they need to do and distracting them from working their other contracts means some other airline gets delayed.
What do you think would happen if say, JAL had a major problem in SIN, and no one could check in for QF flights because SATS had tossed everyone available at fixing the JAL issue?