I wish your mother well. It must be awful having to go through that.
It's an attitude that ignores a passively "hanging out" family member who might just want to hear what's going on, even if they can't interact back. It's like someone quiet at your table: if they are not talking, does that mean they aren't part of the party?
I do kind of disagree with you. There is more than enough debate around death that it cannot be a simple binary state. My experience with loved ones, brain cancer and euthanasia, however, made it clear to me that it's consciousness that matters, not intellect or interaction. The slow decline of the brain resulted in less and less intellect, then less and less interaction, and finally consciousness fading away as well. There was no single point where it was clear that she went from 1 to 0, but at some point you know that the brain, and her consciousness, was irreversibly broken, despite her heart beating on and her lungs working. It's that irreversibility that I find most important - if she will never be conscious again, she will never be alive again, never care or love again, never interact again. There could still be spasms or deep-rooted physical responses like in the article, but what does that matter when there's no mind to witness it?