It is an interesting position. Black could have had seki but he went for this ko. He also played a move just before that should be smaller than defending this corner. It would appear that leaving a ten thousand year ko could be perceived as a closer game. That made me think of when it was claimed that the game couldn't end.
Certainly they would know what to do. For example if there were no moves left on the board and the ko was left to connect, except it is black to move. They would know what to do
I think it would parallel what happened when Iyama and Ichiriki ran out of stones. They knew exactly what to when that happened.
This concept that different ways of losing or winning don't come with the same value exists in many games. Many Go players, for example, don't value much winning on time. Chess players seem to be so embarrassed by being checkmated that it is customary to resign when it is inevitable. I'd think this consideration also played a role in the 1928 game. They didn't want to lose and found it to be a better way of losing to claim the game couldn't end. Having a dispute probably has little value for most players when they are losing but it happens. The idea that the ko isn't finished and therefore the game isn't over is an interesting, if impractical, idea.
In last night's game fighting the ko as black would be impossible but creating it showed spirit. The printed kifu will also be more interesting to look at and this was an interesting game. If you look closely you can see that white has a 60+ stone group that only has two sure eyes. Maybe it will be more rewarding for many to play through it because it ends with a bang.
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kvasir
The dispute was resolved in the end when it was decided that white won and black didn't lose.