Well no. Part of the web is the internet. You can't skip the internet and talk about resource representation caching in REST. But I am talking about the web -- that's why I mentioned how pages are rendered.
HTTP and HTML, while both are fundamental to the web, are also just implementation details. HTTP has evolved a fair bit since its inception for the web (there was no PUT or POST, for example).
To take your analogy, it would be like describing Cocoa library when your wife asks how an app works.
To describe the Internet when someone asks how the web works would be like describing how the iOS works when someone is curious about a specific app.