The video creator was clearly speaking generally about standard, clean modern tracking workflows—not tracking for deliberate saturation.
No, that's absolutely not correct. He was very clear about it:
(Premise) "Mathematically, objectively, every single time in the past, present or future that an engineer has ever tracked through a Neve with no converters clipping and faders at unity it is not possible for there to ever be or have ever been Neve distortion." (and now conclusion) "That means that distortion cannot be an ingredient in the Neve sound".
It would maybe have been as you say, and arguably more correctly, that "as long as you track without pushing a pre to distortion they don't really have 'a sound'", more or less. That would be a nuanced take that would see more reasonable to me.
If you want to debate the actual data and listening tests presented in the video, we can do that. But you have to actually watch the video first or read at least the whole summary of it.
We can talk about what we have seen, which up to this point was the silly presumption that effectively nobody tracks with distorted preamps. Finally someone (you) addressed that by dismissing it as really meaning something else, which at best means it's hyperbole.