As far as the header Referer goes, this header would include the full URL, including protocol. Just like you would see it in the URL field in the browser. For example:
http://www.example.com/this/that/theother.jsp
So, since you are using the URI::host method, this would extract the host and your refer_host variable would be set to www.example.com, if we follow the prior example.
So, if you were using starts_with, you would have to match all possibilities at the beginning of the URL. ie. www.example.com, example.com, goodstuff.example.com, etc.
If you are just interested in a domain (example.com), then I would change the operator to ends_with and just specify example.com as a string or put it in your class.
DeVon