I don't really understand this, I was trained on all the knowledge I was capable of ingesting, but my outputs are largely mine unless there is too much similarity to a copyrighted work. I don't understand why AI would be different. When I do work for hire, my employer owns it, roughly equivalent to me paying Open AI/Anthropic for output.

It's not, barring any secondary issues like proof the training data was acquired illegally.

When there is a copyright dispute, it's always a subjective test on the judge/jury's part as to how similar it is in appearance, purpose, etc. if it's not deemed fair use.