The best pilots I have worked with knew how to fly, knew their aircraft, and knew the rules. They use the rules to their advantage to get the job done, a lot of the job involves working in the grey area and thinking outside the box.
Example above with the aircraft showing 200 kg above MTOW on the lower SD display. The data on the lower on the lower SD display is irreverent. The legal requirement is to check the load sheet against the performance data, if the load sheet is legal, you can go. The numbers on the lower SD display can be in error by 1% due to the way fuel volume and properties are measured and converted into mass then added to the ZFW to generate the numbers on the lower SD screen.
As with the BA crew, I would have done exactly as they did, made an approach and and assessed the conditions for myself. Tower wind is a mean wind of the wind sensors across the field over the previous 120 seconds, the tolerance is +/-10 degrees, and +/-10% above 10 kts measured 10m above the ground. SYD probably has one for every threshold plus mid field.
As an approved observer I am allowed to make an approach and look at the windsock for the runway I intend to land on and decide then to land or not. This is by far the easiest for me, if the windsock is not fully extended it is below 15 kts and it is realtime next to where I will touchdown.
The BA crew could have had a wind indicating 210/22 on the ND which is still 22 kts in the flare, and still perfectly legal to land on 34.