For those who are confused I believe you're referring to the application logo and branding. So basically the Firefox > Iceweasel case again. While the art you create with it is still yours.
Of course anything you make yourself is yours. I'm not sure how the license can confuse anyone into thinking it wouldn't be. It likely wouldn't fly with the law anyway. Unless it was all saas.
You'd be surprised. There are a lot of people out there (and here) who think that unilaterally-declared LLM licenses can dictate what they are allowed to do with the output. Hell, a lot of people think that LLM's can be copyrightable. Copyright law is very clear about the conditions required for copyright protection, and LLMs fail to satisfy at least two. Even failing one is sufficient (see the Smiling monkey case).
