That license is called "All Rights Reserved", in which case you wouldn't be able to legally use the output for anything.
There are research models out there which are trained on only permissively licensed data (i.e. no "All Rights Reserved" data), but they're, colloquially speaking, dumb as bricks when compared to state-of-art.
But I guess the funniest consequence of the "model outputs are a derivative work of their training data" would be that it'd essentially wipe out (or at very least force a revert to a pre-AI era commit) every open source project which may have included any AI-generated or AI-assisted code, which currently pretty much includes every major open source project out there. And it would also make it impossible to legally train any new models whose training data isn't strictly pre-AI, since otherwise you wouldn't know whether your training data is contaminated or not.