GANs are a form of unsupervised learning. They don't have "ground truth" either, just lots of existing images which they learn to imitate and to distinguish from other kinds of images not present in the training set. Similarly, humans learn to distinguish natural images from unnatural ones starting from birth, and use that learned feedback to filter the images produced by our imaginations: a natural example of a GAN. Our input is less… focused, and includes non-visual elements, and there are of course other aspects to general intelligence besides visual processing and imagination, but in this area at least we operate on the same basic principles.
> So for instance, you can't expect to train it on images of manga characters and find that it now draws you in the style of Michelangelo. That's what I mean.
Are we talking about GANs here, or humans? A human trained exclusively on manga wouldn't suddenly develop the ability to imitate Michelangelo either. On the other hand, a GAN trained on manga may sometimes produce images which are not recognizably part of the manga style—which could be seen as an entirely new style. (It would help the process along if you included non-manga images in the training set, as a human would have access to those as well. Then different styles of the same scene just become one more dimension in your "manifold" of all possible images.)
Inventing and learning to draw in a new style isn't something that comes spontaneously to humans. It takes a lot of practice both learning what makes the style distinctive and learning to create art in the new style. A GAN has most of the basic elements required to do the same, but we generally don't use it that way. An interesting experiment might be to permute the discriminator to favor specific elements which were not common in the training set and then train the generator to satisfy the altered discriminator.
> Which means, it can't innovate.
What exactly do you mean by "innovate"? To me the word implies intent, which is clearly out of scope for a mere GAN. Intentional behavior would put it in the domain of an artificial general intelligence or AGI. However, generating images which aren't in the training set is just a matter of choosing a point on the "manifold" which doesn't correspond to any of the input images. Though expecting the GAN to spontaneously invent a distinctive and consistent new style which appeals to humans, without being one itself or otherwise being trained in what humans might find appealing, is a bit much IMHO.
The biggest difference remains the fact that this GAN only has manga for its input, which limits its ability to produce anything outside that context. Its whole life is manga and nothing else. Humans have the same issue with creating things completely unrelated to any prior experience, but they have a much larger and more varied pool of experiences to draw from. (And even then humans can easily get stuck in one particular style and find it difficult to change.)