If a museum can include a small portion of a frame around a public domain painting and claim new copyright as a result - surely any smallest spark or creative influence qualifies, including choosing a single word and choosing the model and time and which output is selected does as well.
The idea of work for hire, and the notion of copyright assignment, applies to people and not machines or processes employed in the creation of a work. Your brush manufacturer would never dare try to claim that their creative selection of fibres and thus their contribution to the unique brush patterns in your painting constitutes a creative contribution to your work. Why is a complex digital model which does the same any different?
Perhaps it is copyright as a whole that is wrong and is nothing to do with AI. This is what we get for creating imaginary property as a means to finance speculative creative endeavours in a capitalist system. So, yeah. Fun times there - once again technology challenges another economic status quo.