I've seen photorealistic generations add (distorted but still somewhat recognisable) watermarks too, because that's what the training data had.

Everything is a derivative work, and always has been. AI is just making that salient fact so much more visible, and now everyone who believes in the delusion of Imaginary Property is scared at that truth revealing itself.

Incidentally, this is also what young humans learning to draw will do. They start by copying what they've seen.

Young humans aren't forging signatures.