Disclaimer: this is purposefully obtuse.
Other effects in the game which explicitly state they kill you:
Shadows, succubi, massive damage, death saving throws, beholder death ray (notably not even their disintegration ray kills you), power word kill, vampires, mind flayers, night hags, drow inquisitors.
Clearly, if they intended for disintegration to kill you, they'd have said so. Since specific overrides general, and there is no general rule that disintegrated creatures are dead, I rest my case. QED.
Crawford's statement there makes it clear that he believes "being turned to dust" kills you. He believes it's so obvious that he doesn't need to explain it. That's why his statement just takes "you're killed" as a given.
The rules aren't written in such a fashion as to very slowly and patiently explain every possible interpretation to you and hold-your hand to finding the correct one. They assume you have a basic reading comprehension. It's not really WotC's job to fix that if it's a failed assumption.
WotC don't issue errata for stuff like this, because they think the argument is facially stupid. If they issued errata for every facially stupid argument, then the errata document would become so large that it'd be unusable - there's an infinite well of dumb takes that don't require an errata to clean up.
That's the job of your DM.