• To have been influenced by that piece, legally, the human will have had to pay the copyright holder to; go to the cinema, buy the bluray, see the performance, go to the gallery, etc. Works out of copyright obviously don't apply here.
• To be trained in a discipline, the human likely pays for teaching by others, and those others have also paid copyright holders to view the media that influenced them aswell

Neither of these are necessarily true, and the first one is even demonstrably false given the amount of copyrighted content that can be freely accessed online.

• Even thought the vast majority of art is influenced by all other art, humans are capable of novel invention- ie things which have not come before - but GenAI fundamentally isn't.

That depends highly on your definition of "novel invention". Given that GenAI can be given randomised noise as input to create something from, it's highly debatable if GenAI is truly "incapable" of novel invention. And even then, it's possible to provide prompts describing a novel style (e.g. "oil painting with thick, vibrant streaks of colour" or something), so a human + GenAI together may well be capable of novel invention. I don't recall the last time a human was able to create something that could not be expressed in previously existing words at all. You can describe Van Gogh without using his name, or describe a Picasso without using named art styles. Yet we consider their works novel, no?

That's the reason people are complaining, cos they aren't being paid today, and they won't be paid tomorrow.

Even if AI only trained on non-copyrighted art, this would still be true. It might set the AI companies back a year or two, but AI art generation is here to stay and will threaten artists' incomes. These lawsuits are only really stalling tactics to delay the inevitable.

I can't predict if they're going to win their lawsuit or not, nor do I know if they should. But the artists' salvation won't lie in copyright law, I know that much.