To someone only weakly aware in this area, can you explain what is wrong with the statement? From a cursory view, these protocols indeed seem to normally carry the mentioned payloads.
There are a few bits that don't make sense eg cookies where the server sends something and the client is expected to remember it but they can just be ignored.
Also, as a minor point, even when browsing the web, a minority of the actual requests deliver HTML -- most of them are for various kinds of media referenced by the HTML document.