This is better, but your approach is still very flawed. It still asserts that since you think there's a possibility that one of the two categories of play is arbitrarily defined as all things NOT A that it cannot be disentangled from A and therefore the entire categorization is of limited value since it's just bins for A and NOT A according to some arbitrary distinction.
The problem here, I see, is not that backstory-first is actually arbitrary - it has valid descriptive power for how games work - but that there are a number of sub-approaches that create different results. This is not indicative of an arbitrary distinction, though, but rather that there are other distinctions that apply within the scope of backstory-first. There is not an argument being made that says all play is clearly separated and delimited by the analysis of situation/backstory first, so the complaint that this distinction doesn't clearly delimit is logically flawed -- it hasn't been suggested that it does. In fact, there's been quite a good bit of talk about how various backstory-first approaches can be separated further with other analyses.
The sum total of your argument here seems to be that since situation-first vice backstory-first doesn't do all possible categorizations of play, it's therefore at least partially arbitrarily defined as A and NOT A. You're totally ignoring that backstory-first does do work in explaining how play occurs, it just doesn't do all of the possible work.
Again, there are a number of backstory-first approaches, and if you'd like to discuss them (I offered this earlier) we absolutely can talk to differences in Trad, Classical, NeoTrad and OSR play. There are distinctions here that are rather important as to how the game uses backstory-first.
Finally, the middle bit where you question if
@pemerton is qualified to examine backstory-first play is an appeal to authority. You're not evaluating the argument, but suggesting that the person lacks sufficient experience for their analysis to be useful. This may be true (it's why it's an informal fallacy), but you didn't do any work to show that the analysis was, in fact, incorrect or wrong. I've often told others that they lack the experience to inform their assertions, but I do so after showing that the assertions are badly flawed and without foundation. Go for the argument first -- show why
@pemerton has failed to show what he claims -- then you can suggest reasons why. Here, though, you're totally wrong --
@pemerton has clearly stated that they have extensive experience with backstory-first. The claim that they don't do much of that play is a now thing -- he doesn't do it now. Hence why he defers on system-specific arguments regarding 5e or other games he does not play.