I still incline to the view that, if no one can remember it, it doesn't matter. Conversely, a necessary condition of something being relevant is that it can be remembered by those at the table. If the players don't remember something, they're not going to leverage it (which is the case that I was responding to in my post that you quoted).
I'm not saying that GMing doesn't require any note-taking - it may or it may not, depending on context and circumstances, how much of what matters is recorded on various sheets (eg do we need to note that so-and-so suffered a broken shoulder if
broken shoulder is a condition recorded on the appropriate character sheet?), etc. But I think the degree of note-taking required can be exaggerated, and that the idea that it is necessary to so for the players to leverage some detail doesn't seem right for me.
Nor do I think the degree of prep really helps here. The main thing that needs to be noted is
stuff that matters and
stuff that changes. And that is likely to have to be done even if there is prep. In my personal experience, doing prep doesn't change the amount of session notes I need to take.
I already posted upthread that (in my view) the main challenge in GMing is juggling the fiction. The scenario you have set out is an example of that. But it doesn't seem to bear upon the prep issue or whether extensive notes are particularly necessary in a low-prep game (which is what I was discussing with
@Imaro): given what I've bolded, I don't see how this shows that preparation is necessary or makes things easier.
Even if the existence of the miner was recorded in some pre-authored notes, you would have to record the interaction with the paladin and it's significance.
To me this example does seem to relate to a different aspect of this conversation, namely,who is responsible for driving play. There are systems in which the paladin's treatment of the NPC would be something that the player is responsible for recording on the PC sheet in some form. Even if that's not the case (eg D&D PC sheets tend not to have a "relationships" box), if the player does hope to leverage this relationship down the track then I would expect him/her to make a note of it. But as you present it this doesn't seem to be an instance of extensive notes being required; it doesn't seem that prep would have made any difference; and your reason for making the notes is not that the players are going to leverage something later on.
It just seems to be an example of a GM keeping track of material to use for subsequent framing and consequences, which are some of the aspects of "fiction juggling" that I identified upthread.