An example apache virtual host config for internal proxying. A wonderous hack if you lack control of DNS servers and need to test a site on a device that doesn't let you modify the hosts file.

10.0.0.10.conf

<VirtualHost *:80>
        ServerName 10.0.0.10

        # Set url to proxy
        ProxyPass / http://hosts.domain.dev/
        ProxyPassReverse / http://hosts.domain.dev/

        # Set location
        <location />
                # Set url
                ProxyPass http://hosts.domain.dev/

                # Ouput html from proxy filter
                SetOutputFilter proxy-html

                # Add referer hack (if the site uses referrer as security)
                Header add referer "http://hosts.domain.dev"
                RequestHeader set referer "http://hosts.domain.dev"

                # Overwrite html, exchange urls with proxied (like href, src, etc.)
                ProxyHTMLExtended On
                ProxyHTMLURLMap http://hosts.domain.dev  http://10.0.0.10
		
		# For items that use style="background-image:url()"
		ProxyHTMLEvents style

		# You can add more url maps to overwrite if there are subdomains
		# that you want/need to override
                ProxyHTMLURLMap http://static.domain.dev  http://10.0.0.10

                # Rewrite Cookie domain if the site uses sessions as an identifier
		# i.e. PHPSESSID
                ProxyPassReverseCookieDomain .domain.dev 10.0.0.10
        </location>
</VirtualHost>

@DieselDriver I can't say why it's not working without setting it up, but my initial hunch would be that not all the requests are made against medium.com but through other hosts, e.g. cdn's etc. You'd probably have to set up proxies against those URL's as well.

The relevant request for the main content is made against medium.com and I think they check the referer in other way as usual.
It's an interessting problem - this is the first website that makes troubles with a reverse proxy. :-(