I feel like you’re making the same argument as me, with the same rhetoric, but a different example. No, I do not think the printing press, paint, or generative tools are bannable by copyright. I do think all 3 could be used to produce a work that is in violation of copyright. And no, I don’t think a novel work produced by any of them are in violation of copyright.
If a printing press randomly produces Hamlet, you cannot sell it. That does not mean you cannot generate something that is sellable without violating copyright by printing random words.
There is a small amount of attention paid to whether an artist knew of a work that someone claims was copied. Especially in the literary world with hacks who try to steal from successful authors with pathetic claims.
But they tend not to hold a lot of weight. It just makes it easier to dismiss trolls.
AI is a tool. It is not sentient. It is paint.
But yes, the claim about an artist owning an entire style sounds pretty off to me. There's no way Picasso has a copyright claim on every cubist painting ever made, nor does Van Gogh own every painting containing a sunflower.