I have the impression this is a workaround but not a solution. If you access your site via github.com, you want the content of readme.md displayed, so people know, what this project is about. If people access your website via github.io, you want the content of index.html displayed. I was under the impression, that the right way to do this, is to exclude README.md from your website by including in your _config.yml:
Now the problems seems to be, that this is not always working as it should.