Id call the inner movements of data within google/facebook private networks part of the internet. When i do a google search, or watch a youtube vid, i know i am generating more traffic than the http requests and answer from the edge of google's network. The inner workings of the largest private networks often service the internet, if not by name, and therefore should be included in its total bandwidth. But good luck measuring it.
While it may be that a good chunk of private traffic is in the service of internet services, I think calling it 'the internet' is wrong technically and in spirit.
The spirit and technical definition is that fundamentally the internet is a connection between private networks. Initially it was some universities, ARPA and so on. Now it's Google, Facebook, Verizon, Amazon, AT&T and so on.
What happens on these networks is private network traffic. If some of that traffic travels long distances it doesn't make it less private. Why count inter-region traffic of cloud providers, why not count the inter-AZ traffic of AWS regions? Why not count the inter-rack traffic and so on. The difference between the internet and private networks is not about distance travelled it's about ownership. For instance if traffic goes between Google and AWS at a peering location in CA, then that is internet traffic even if the data doesn't go very far.
