I think that the discrepency might be due to your counting the whole trip as discount economy however the domestic flights within Australia will have been on full economy SC earning ( since K domestics earn Full SCs )

I do calculate that he could have earned 23918 qmiles and qpoints when crediting to AA ( assuming he had ensured the use of QF flight numbers except on YYZ-LHR ) ( the drop to 23918 is due to the only earning 25% miles on BA )

Whether credited to AA or QF, they both would have brought him to similar distance towards renewal 46.7% QF vs 47.8% AA

Where the big difference would come in is in spending miles

Crediting to QF as a gold member ( 50% bonus ) he would have earned approx 37322 spending miles

Crediting to AA as a platinum member (100% bonus) be would have earned approx 47836 spending miles

In calculating the above, I allowed for the 25% earning on the BA flight from YYZ-LHR and postulated that if crediting to AA, the traveller would have used the QF flight number rather than the BA one when travelling from UK-Oz

So, although status renewal %s met are similar, the value of the spending miles is (imo) a lot higher. The earning on AA is
53.15% of a Y r/t from UK-Oz (90k required)
39.86% of a J return from UK-Oz (120k required)
29.90% of a F return from UK-Oz (160k required)

Compare with QF where the 37322 is

30.01% of a Y r/t (128k required)
15% of a J r/t (256k required)
9.7% of a F return from UK-Oz (384k required)

I would say that since in both cases it would earn 47% of the renewal requirements for Sapphire status, that the amount and value of the miles earned would have been far better accrued to AA )

Dave