Not possible to reliably tell apart. The Image generation scene is one thing. For a lot of output, there are still some tells. Text generation though...well good luck ever finding that out.
It sounds like the honor system, which is not unprecedented. A lot of governmental systems rely on people to tell the truth when interacting with the government, and then they have to police cases of suspected fraud after the fact. If you were dragged into a copyright suit by someone, you could probably try to prove that the work was AI generated as a defense? Not sure how effective it would be.
It would probably be similar to when wordperfect was sued for including famous painting as clipart. WordPerfect won using basically this defense (that no human creativity went into making the clip art) https://en.m.wikipedia.org/wiki/Bridgeman_Art_Library_v._Cor....