If I take pretrained imagenet and just make it wider with nodes with random weights and biases, I can still feed the network an image and get a reasonably correct label as an output. In this example I could obviously point at the nodes from the original imagenet and say that those do the image recognition, we know the rest of the network doesn't contribute anything but noise.

On a technical level of course the whole network contributed to the output. In everyday reasoning and language however we usually focus on the parts that matter to a reasonable degree and ignore the rest. A sack of rice falling over in 2005 might have contributed to the 2008 financial crisis. With the world being an analog network of particles it even seems obvious that that sack of rice must have had some infinitesimal influence one way or the other, it's just more practical to ignore it.