You can easily see if you are off or not and you aren't focused on your sword, but what is beyond the sword. Sensei has us do that in the dojo to gauge how straight our cuts are. Seems to work because your looking further off into the distance.
I'm guessing, but I think it works exactly because you aren't
focusing on the sword. (it's the attention not the visual part)
Ever notice that if you are holding something important, and you have to put it in an important (precise) place, you might start your move fine, but as soon as you get near the final place and go slow and careful, your hand starts to shake? I work with my hands so I've seen this happen to me.. but if I trust that I can do it without worrying about it, I can stop over-concentrating on my hand's location at the critical moment (make it just like a few seconds earlier, when I was only reaching toward the target), and my hand moves smoothly.
I know it's ki related but it's hard to parse it out. Maximal qi engagement with minimal li usage might be a Chinese-terminology way of saying it.