You can prompt/train the AI to add a couple of random minor errors. They're trained from human text after all, they can pretend to be as human as you like.
I'm listening to a slightly wonky early James Brown instrumental right now, and there's certainly a lot more error than you'd get in sequenced computer music (or indeed generated music) but the force with which humans wrest the wonkiness toward an idea of groove is palpable. Same with Zeppelin's 'Communication Breakdown' (I'm doing a groove analysis project, ok?).
I can't program the AI to have intention, nor can you. If you do, hello Skynet, and it's time you started thinking about how to be nice to it, or else :)
This is as everything else, machine produced has a flawlessness along some dimension that humans tend to lack.