Depends on the training and the output.
Just like if you photographed the Mona Lisa in such a way as it recreated the piece as if it wasn't a photograph, a model sufficiently trained that can reproduce the original training data, you have copyright issues.
Problem is that many models can do this, but it's a mathematically improbable occurrence.
If I make a stamp that's made of 1 billion exact copies of different copyrighted photos and cut it infinitesimally small, and mixed it up, the problem that it can produce the original work that it was made from still becomes a copyright issue.
You'd have to prove the opposite, in fact. That it's mathematically impossible for your model to reproduce the copyrighted content for it not to be an issue
Man I wonder how they set it up to where they don't know who runs it