No that’s not… at least in many countries. Unlike patents, “parallel creation” is allowed, this was fought out in case law over photography decades ago, because photographers would take images of the same
subject, then someone else would, and they might incidentally capture a similar image for lots of reasons and thus before ubiquitous photography in our pockets, when you had to have expensive equipment or carefully control the lighting in a portraiture studio to get great results… well it happened and people sued like those with money to spare for lawyers are want to do, and thus precedent has been established for much of this. You don’t see it a lot outside photography but it’s not a new thing for art copyright law and I think the necessity of the user to provide their own input and get different outcomes outside of extremely sophisticated prompt editing… will be a significant fact in their favour.
It's bad news for art websites themselves if that's the case...