Well, copyright claims are usually a civil matter (in the US at least). For a civil dispute you have to make a judge or jury believe you more than the other person.
replyBut it sounds like you are talking about a criminal charge. There the bar is higher and the government has to prove beyond a reasonable doubt. In that case I suppose the government could do things like search your computer, subpoena the AI companies for their records, talk to your editor, talk to your family and friends, etc... All the usual stuff.
Before you would ever get to a point where someone claiming your work was AI would be able to get access to your computer, editor, family/friends, etc there would need to be a bar that needs to be cleared for a judge to allow that discovery to take place.
replyWhat I'm asking is what is that bar?
Copyright is going to be assumed by default - in order to break that assumption there needs to be some process... however for all the people who are "concerned" about the copyright status of works that have touched AI I've never seen anyone make a feasable argument on how it would ever practically take place.