An interesting question. A million input neural network isn't necessarily absurd. Images are very high dimensional. One could easily imagine a one megapixel input to a neural net. But in natural images no single pixel is indicative of any single image characteristic by itself. I think this isn't a coincidence but a common characteristic of "natural" high dimensional data, on which neural nets tend to work well. So yes, I'd say what you've described is not likely for a large category of "natural" high dimensional data which probably includes most of the data we care about in the real world.