Sorry to be that guy, but the AI hype is getting out hand. COSYNE this year was packed with papers comparing deep learning to the brain... it drives me nutty. Convnets can be reasonably put into analogy with the visual system.... because they were inspired from it. But that's about it.
To address your actual comment: I would argue that this is not really interesting or surprising (at least to the ML practitioner), it is very well known that neural nets are incredibly sensitive to initialization. Think of it like this: as training progresses, parameters of neural nets move along manifolds in parameter space, but they can get nudged off of the "right" manifold and will never be able to recover.
Sorry for the rant, the AI hype is just getting really out of hand recently.
Machine learning is specifically not magic. Blackboxes are not useful. Convnets work so well because they build the symmetries of natural scenes directly into the model - natural scenes are translation invariant (as well as a couple of other symmetries), anything that models them sure as hell better have those symmetries too, or you're just crippling your model with extra superfluous parameters.