Earlier quoted context omitted.
Yes, check out "attention" mechanisms. The network can use wide convolutions for the image as a whole, effectively mixing data kind of like a blur function, and also use finer convolutions for a small piece of the image that it chooses to focus on.
Does the problem of elephants still exist with such approach? It doesn't seem right that an unexpected feature in a corner of the image would have a dramatic impact on the recognition of the features elsewhere.
So the dramatic changes seen in the image seem to be artifacts of the visualization and not of the network's performance.