Background
Around 12 years ago, I started running analytics for all my websites myself, through the use of AWStats. I know it was working pretty well up until about 2013, at which point I stopped paying attention for several years. Now in February, 2018, I got curious again and went back. At first I thought my installation had failed, because the referral sites listing was so sparse. I reinstalled and reconfigured AWStats only to get the same result. Upon researching, I found out that web standards and web-browser client software has (as is typical with the world) changed and rotted my setup!
Referrer No Longer Really a Thing
These days the referrer header rarely makes it through for 2 main classes of reasons [0].
1. Requests transiting across HTTP <-> HTTPS boundaries do not include the referrer header.
2. The referrer header is frequently disabled by sites (especially search engines and high-traffic sites) through the use a special HTML header meta control tag [1]:
<meta name="referrer" content="no-referrer" />
Worry not, though. When client-side Javascript is enabled, ga.js still sends enough information that Google can reconstruct most of everyone's browsing sessions on their backend. Now Google (and only Google) really has all your / our data (generally speaking). :-\
[1] https://stackoverflow.com/questions/6880659/in-what-cases-will-http-referer-be-empty
[0] https://stackoverflow.com/questions/6817595/remove-http-referer