My opinion is that the gh-pages is a trick by GitHub to allow you to create a website for the project. So the concept of branches somehow get a bit lost there.
It happened to me as well, that sometimes they end being pretty different with the original project. You may try to find trick to organize them better but don't get it confused git the general concept of branches.
Imagine, for example, a project with pre-compiled elements (SASS for example), they probably wont be included in your project, but they may be needed in the gh-pages branch.
Keeping the GH pages in sync with the README is due to this diversion between GH pages and main project, it may occur that you forget about one of them. The advice of keeping then in sync is more common sense related with keeping your project organized than anything else.
I wouldn't get worried if they don't have any resemblance.
As I said, this is only my opinion.