Part of the issue here might also be how we understand which move “starts a ko”. In this variation, which move is the one “starting the ko”?
Is it 3, allowing white to capture the ko? Or is it not until white’s next move at E4 that the ko is officially started? Or is it black 1, initating the sequence which leads to the ko? Then maybe white E2 “started the ko”? But what if E2 was played a long time ago, and it was much later that black chose to initiate the ko with 1?
It turns out that this notion of who decides when it’s time to start it is more useful than what particular move takes the ko first. In this case, black would never play 1 without planning to follow up with 3, so we can safely say that 1 “starts the ko”. (well, it attempts to start it, white could just play elsewhere…)
To see the same idea applied in a different context, consider any tsumego where black can play first to make the result ko, like this one:
The correct sequence for both sides looks like this:
So it’s not until move 7 that we have an actual ko on the board, but we would still say that move 1 is the one that “starts the ko”, because the local sequence after that is a one-way-street.
Edit: Actually, let’s be more precise like this: Black 1 indicates that black would like to attempt to kill the corner. It’s saying “hey white, I want this corner, will you fight me over it?”. White may accept the fight immediately, or play elsewhere. If both sides plays elsewhere for a few moves, then white comes back to start the ko sequence, we would also say that that white move started the ko. So anyways, language is messy, and maybe not the main point here. Sorry if I confused things unnecessarily