Sure, I wasn't trying to make a declaration of what is true, just stating my experience with the terms (which is why i refer to myself as a middle schooler, having come into the game with BECMI in 1985).This is definitely a point of confusion for a lot of folks.
I'm among the folks who often point to Dragonlance as a transition/inflection point. From TSR focusing less on challenge/exploration-focused modules, to more on heroic adventure story-style modules, and novels alongside them. The so-called Hickman Revolution.
A lot of the hardcore AD&D partisans will exclude DL and 2nd ed AD&D from the old school, and so some extent they're right. But on the other hand, as The Elusive Shift and early fanzines document, some folks were doing very story and character-focused D&D in the 70s, nearly from the get-go.
While "story-focused" isn't the first phrase that I'd normally pair with "old school", I don't think it's incoherent either. Some old schoolers were story focused. I think this mode of play is often referred to as "Trad", as opposed to "Classic", which is ostensibly the Gygaxian challenge-focused style.