Interesting point - usually people approach the question "who draws the tiger" from the other end. As in, the assumption is (not unreasonably!) the genAI is doing all the work and the AI 'artist' is doing nothing.

Of course, the more control you have - as you say - over the process, the more you are the artist.

I have to say, I'm not that interested in whether the output 'really' is art or not. I'm sympathetic to non-AI artists and I personally prefer art made by humans. However ... it is not impossible to make something that looks good or communicates an interesting idea with AI, but not trivially.