100% agree that this is what it should be called. To argue that big websites being big makes them equivalent to the whole Internet is absurd. Besides, I love the idea of the only recourse to be to go back to independently run information websites.
For the younger generation, social sites are the internet. They open an app on their device, they don't go to sites by searching the web. I've seen people perform a web search in an app store thinking it was the same thing.