You make some good points, but I personally think it's similarly naive to think that we cannot eventually get to a point, where an artificial intelligence produces results so similar to a human in some areas, that the fact that it functions differently becomes irrelevant.
In fact I'd say that current neural networks are a big step forward both in terms of the results they produce and in terms of how similarly they work to a brain. We know that artificial "neurons" are a distant abstraction of how a brain works, but a neural net is not just a normal mathematical algorithm. Yes, it's "just" matrix multiplications, but at the same time the complexity of the computation is so far beyond what any human could analyze or design that it's a blackbox. That in particular is similar to a real brain.
The output of a neural network is deterministic just like with a "normal" algorithm - two identical inputs give you two identical outputs. With the case of image generation algorithms part of the input is noise (in the shape of the final image), which dictates how will the final image look. Change the noise very slightly and the output can be completely different. Since we want the results to be reproducible, we use a pseudorandom noise generator initialized by a seed number. Same seed will produce the same noise pattern and therefore the same resulting image.
What if we instead use a noise generator that is truly stochastic? We are able to do that (using specialized hardware). The algorithm itself would still be deterministic, but it would be unpredictable because a part of the input would be unpredictable. Would that be "organic" enough?
And what if we stop computing the neural network on a GPU and instead use a chip that does analog matrix multiplication (already exists, although not powerful enough for this particular usecase, yet), which brings a stochastic element into the computation itself? The computation itself is no longer deterministic. You know what will roughly happen, but cannot predict the exact result even if you know the input.
Would that be organic enough? It is certainly a very different thing now from how any normal computations work.