That's the ideal and how it's advertised, but in reality they retain a lot more of the original copies than most people think, in addition to the fact that the output is often not sufficiently "transformative" in copyright terms to avoid being considered a derivative work still needing a copyright license.

In your Mario example, the character as such is unique enough that it has its own copyright and you can't use images of that character commercially without a license regardless of how the image was created. If it's recognizable as Mario then you copied the design as far as a judge would be concerned. If you asked a human to draw it then it would be equally infringing.

A human doesn't even need to ask for a copyrighted work for it to generate infringing outputs.